Since the last century, various predator-prey systems have garnered widespread attention. In particular, the predator-prey systems have sparked significant interest among applied mathematicians and ecologists. From th...Since the last century, various predator-prey systems have garnered widespread attention. In particular, the predator-prey systems have sparked significant interest among applied mathematicians and ecologists. From the perspectives of both mathematics and biology, a predator-prey system with the Allee effect and featuring the Bazykin functional response has been established. For this model, analyses have been conducted on its boundedness, the properties of its solutions, the existence of equilibrium points, as well as its local stability and Hopf bifurcations.展开更多
In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifu...In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.展开更多
In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial...In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.展开更多
In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center man...In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases （within a limited value）. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given.展开更多
We propose and study a discrete host-parasitoid model of difference equations with a spatial host refuge where hosts in the refuge patch are free from parasitism but undergo a demographic strong Allee effect.If the gr...We propose and study a discrete host-parasitoid model of difference equations with a spatial host refuge where hosts in the refuge patch are free from parasitism but undergo a demographic strong Allee effect.If the growth rate of hosts in the non-refuge patch is less than one,a host Allee threshold is derived below which both populations become extinct.It is proven that both populations can persist indefinitely if the host growth rate in the non-refuge patch exceeds one and the maximum reproductive number of parasitoids is greater than one.Numerical simulations reveal that the host refuge can either stabilize or destabilize the host-parasitoid interactions,depending on other model parameters.A large number of parasitoid turnover from a parasitized host may be detrimental to the parasitoids due to Allee effects in the hosts within the refuge patch.Moreover,it is demonstrated numerically that if the host growth rate is not small,the population level of parasitoids may suddenly drop to a small value as some parameters are varied.展开更多
In this paper, an algae-fish harvested model with Allee effect was established to further explore the dynamic evolution mechanism under the influence of key factors. Mathematical theoretical work not only investigated...In this paper, an algae-fish harvested model with Allee effect was established to further explore the dynamic evolution mechanism under the influence of key factors. Mathematical theoretical work not only investigated the existence and stability of all possible equilibrium points, but also probed into the occurrence of transcritical and Hopf bifurcation. The numerical simulation works verified the effectiveness of the theoretical derivation results and displayed rich bifurcation dynamical behaviors, which showed that Allee effect and harvest have played a vital role in the dynamic relationship between algae and fish. In summary, it was expected that these research results would be beneficial for promoting the study of bifurcation dynamics in aquatic ecosystems.展开更多
The aim of this paper is to investigate the dynamic behaviors of fractional-order logistic model with Allee effects in Caputo-Fabrizio sense.First of all,we apply the two-step Adams-Bashforth scheme to discretize the ...The aim of this paper is to investigate the dynamic behaviors of fractional-order logistic model with Allee effects in Caputo-Fabrizio sense.First of all,we apply the two-step Adams-Bashforth scheme to discretize the fractional-order logistic differential equation and obtain the two-dimensional discrete system.The parametric conditions for local asymptotic stability of equilibrium points are obtained by Schur-Chon criterion.Moreover,we discuss the existence and direction for Neimark-Sacker bifurcations with the help of center manifold theorem and bifurcation theory.Numerical simulations are provided to illustrate theoretical discussion.It is observed that Allee effect plays an important role in stability analysis.Strong Allee effect in population enhances the stability of the coexisting steady state.In additional,the effect of fractional-order derivative on dynamic behavior of the system is also investigated.展开更多
In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functio...In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functional response,which is neither differentiable nor locally Lipschitz at the predator axis.This kind of functional response is an extension of the so-called square root functional response,used to model systems in which the prey have a strong herd structure.We study the behavior of the solutions in the first quadrant and the existence of limit cycles.We prove that,for a wide choice of parameters,the solutions arrive at the predator axis in finite time.We also characterize the existence of an equilibrium point and,when it exists,we provide necessary and sufficient conditions for it to be a center-type equilibrium.In fact,we show that the set of parameters that yield a center-type equilibrium,is the graph of a function with an open domain.We also prove that any center-type equilibrium is stable and it always possesses a supercritical Hopf bifurcation.In particular,we guarantee the existence of a unique limit cycle,for small perturbations of the system.展开更多
Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-pred...Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-predator system.On the other side,the Allee effect among prey may cause the system to become unstable.In this paper,a difusive prey predator system with cooperative hunting and the weak Allee effect in prey populations is discussed.The linear stability and Hopf-bifurcation analysis had been used to examine the system's stability.From the spatial stability of the system,the conditions for Turing instability have been derived.The multiple-scale analysis has been used to derive the amplitude equations of the system.The stability analysis of these amplitude equations leads to the formation of Turing patterns.Finally,numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D.The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impacton species distribution.展开更多
In this paper,we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population.Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey popul...In this paper,we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population.Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population.The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail.Hopf bifurcation including its direction and stability for the model is also studied.We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system.It is also observed that for a fixed strength of fear,an increase in the Allee parameter makes the system unstable,whereas an increase in prey refuge drives the system toward stability.However,higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction.Further,we explore the variation of densities of the populations in different bi-parameter spaces,where the coexistence equilibrium point remains stable.Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software.展开更多
In an environment,the food chains are balanced by the prey-predator interactions.When a predator species is provided with more than one prey population,it avails the option of prey switching between prey species accor...In an environment,the food chains are balanced by the prey-predator interactions.When a predator species is provided with more than one prey population,it avails the option of prey switching between prey species according to their availability.So,prey switching of predators mainly helps to increase the overall growth rate of a predator species.In this work,we have proposed a two prey-one predator system where the predator population adopts switching behavior between two prey species at the time of consumption.Both the prey population exhibit a strong Allee effect and the predator population is considered to be a generalist one.The proposed system is biologically well-defined as the system variables are positive and do not increase abruptly with time.The local stability analysis reveals that all the predator-free equilibria are saddle points whereas the prey-free equilibrium is always stable.The intrinsic growth rates of prey,the strong Allee parameters,and the prey refuge parameters are chosen to be the controlling parameters here.The numerical simulation reveals that in absence of one prey,the other prey refuge parameter can change the system dynamics by forming a stable or unstable limit cycle.Moreover,a situation of bi-stability,tri-stability,or even multi-stability of equilibrium points occurs in this system.As in presence of the switching effect,the predator chooses prey according to their abundance,so,increasing refuge in one prey population decreases the count of the second prey population.It is also observed that the count of predator population reaches a comparatively higher value even if they get one prey population at its fullest quantity and only a portion of other prey species.So,in the scarcity of one prey species,switching to the other prey is beneficial for the growth of the predator population.展开更多
In this paper, we study some predator-prey system with Allee effect for prey. In addition, we discuss the properties of equilibrium points and the existence and uniqueness of limit cycle.
In this paper, we are concerned with a predator-prey model with Holling type Ⅱ functional response and Allee effect in predator. We first mathematically explore how the Allee effect affects the existence and stabilit...In this paper, we are concerned with a predator-prey model with Holling type Ⅱ functional response and Allee effect in predator. We first mathematically explore how the Allee effect affects the existence and stability of the positive equilibrium for the system without diffusion. The explicit dependent condition of the existence of the positive equilibrium on the strength of Allee effect is determined. It has been shown that there exist two positive equilibria for some modulate strength of Allee effect. The influence of the strength of the Allee effect on the stability of the coexistence equilibrium corresponding to high predator biomass is completely investigated and the analytically critical values of Hopf bifurcations are theoretically determined.We have shown that there exists stability switches induced by Allee effect. Finally, the diffusion-driven Turing instability, which can not occur for the original system without Allee effect in predator, is explored, and it has been shown that there exists diffusion-driven Turing instability for the case when predator spread slower than prey because of the existence of Allee effect in predator.展开更多
Mass production of black soldier fly,Hermetia illucens(L.)(Diptera:Stra-tiomyidae),larvae results in massive heat generation,which impacts facility management,waste conversion,and larval production.We tested daily sub...Mass production of black soldier fly,Hermetia illucens(L.)(Diptera:Stra-tiomyidae),larvae results in massive heat generation,which impacts facility management,waste conversion,and larval production.We tested daily substrate temperatures with dif-ferent population densities(i.e.,0,500,1000,5000,and 10000 larvae/pan),different pop-ulation sizes(i.e.,166,1000,and 10000 larvae at a fixed feed ratio)and air temperatures(i.e.,20 and 30℃)on various production parameters.Impacts of shifting larvae from 30 to 20℃on either day 9 or 11 were also determined.Larval activity increased substrate tem-peratures significantly(i.e.,at least 10℃above air temperatures).Low air temperature favored growth with the higher population sizes while high temperature favored growth with low population sizes.The greatest average individual larval weights(e.g.,0.126 and 0.124 g)and feed conversion ratios(e.g.,1.92 and 2.08 g/g)were recorded for either 10000 larvae reared at 20℃or 100 larvae reared at 30 C.Shifting temperatures from high(30℃)to low(20℃)in between(~10-d-old larvae)impacted larval production weights(16%increases)and feed conversion ratios(increased 14%).Facilities should consider the impact of larval density,population size,and air temperature during black soldier fly mass production as these factors impact overall larval production.展开更多
We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competitio...We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar compet- itive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.展开更多
This paper proposes a diffusive predator-prey model with Allee effect,time delay and anti-predator behavior.First,the existence and stability of all equilibria are analyzed and the conditions for the appearance of the...This paper proposes a diffusive predator-prey model with Allee effect,time delay and anti-predator behavior.First,the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied.Using the normal form and center manifold theory,the formulas which can determine the direction,period and stability of Hopf bifurcation are obtained.Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations,and anti-predator behavior can greatly improve the stability of the coexisting equilibrium.展开更多
In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive ini...In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive initial value.Then,under certain conditions,this solution is proved to be stochastically ultimately bounded.Furthermore,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of stationary distribution with ergodicity.The conditions for the extinction of infected avian population are also analytically studied.These theoretical results are conformed by computational simulations.We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model.By scanning different noise intensities,we observe that large noise can cause extinction of infected avian population,which suggests the repression of noise on the spread of avian virus.展开更多
Regarding delay-induced predator-prey models, much research has been done on delayed destabilization, but whether delays are stabilizing or destabilizing is a subtle issue. In this study, we investigate predator-prey ...Regarding delay-induced predator-prey models, much research has been done on delayed destabilization, but whether delays are stabilizing or destabilizing is a subtle issue. In this study, we investigate predator-prey dynamics affected by both delays and the Allee effect. We analyze the consequences of delays in different feedback mechanisms. The existence of a Hopf bifurcation is studied, and we calculate the value of the delay that leads to the Hopf bifurcation. Furthermore, applying the normal form theory and a center manifold theorem, we consider the direction and stability of the Hopf bifurcation. Finally, we present numerical experiments that validate our theoretical analysis. Interestingly, depending on the chosen delay mechanism, we find that delays are not necessarily destabilizing. The Allee effect generally increases the stability of the equilibrium, and when the Allee effect involves a delay term, the stabilization effect is more pronounced.展开更多
文摘Since the last century, various predator-prey systems have garnered widespread attention. In particular, the predator-prey systems have sparked significant interest among applied mathematicians and ecologists. From the perspectives of both mathematics and biology, a predator-prey system with the Allee effect and featuring the Bazykin functional response has been established. For this model, analyses have been conducted on its boundedness, the properties of its solutions, the existence of equilibrium points, as well as its local stability and Hopf bifurcations.
文摘In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.
基金Acknowledgments The authors thank the editor and referees for their valuable comments and suggestions. This work is supported by the National Basic Research Program of China （2010CB732501） and the National Natural Science Foundation of China （61273015）, the NSFC Tianyuan Foundation （Grant No. 11226256） and the Zhejiang Provincial Natural Science Foundation of China （Grant No. LY13A010010）, Zhejiang Provincial Natural Science Foundation of China LQ13A010023）.
文摘In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.
基金Supported by the National Natural Science Foundation of China (No. 11071066)
文摘In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases （within a limited value）. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given.
文摘We propose and study a discrete host-parasitoid model of difference equations with a spatial host refuge where hosts in the refuge patch are free from parasitism but undergo a demographic strong Allee effect.If the growth rate of hosts in the non-refuge patch is less than one,a host Allee threshold is derived below which both populations become extinct.It is proven that both populations can persist indefinitely if the host growth rate in the non-refuge patch exceeds one and the maximum reproductive number of parasitoids is greater than one.Numerical simulations reveal that the host refuge can either stabilize or destabilize the host-parasitoid interactions,depending on other model parameters.A large number of parasitoid turnover from a parasitized host may be detrimental to the parasitoids due to Allee effects in the hosts within the refuge patch.Moreover,it is demonstrated numerically that if the host growth rate is not small,the population level of parasitoids may suddenly drop to a small value as some parameters are varied.
文摘In this paper, an algae-fish harvested model with Allee effect was established to further explore the dynamic evolution mechanism under the influence of key factors. Mathematical theoretical work not only investigated the existence and stability of all possible equilibrium points, but also probed into the occurrence of transcritical and Hopf bifurcation. The numerical simulation works verified the effectiveness of the theoretical derivation results and displayed rich bifurcation dynamical behaviors, which showed that Allee effect and harvest have played a vital role in the dynamic relationship between algae and fish. In summary, it was expected that these research results would be beneficial for promoting the study of bifurcation dynamics in aquatic ecosystems.
文摘The aim of this paper is to investigate the dynamic behaviors of fractional-order logistic model with Allee effects in Caputo-Fabrizio sense.First of all,we apply the two-step Adams-Bashforth scheme to discretize the fractional-order logistic differential equation and obtain the two-dimensional discrete system.The parametric conditions for local asymptotic stability of equilibrium points are obtained by Schur-Chon criterion.Moreover,we discuss the existence and direction for Neimark-Sacker bifurcations with the help of center manifold theorem and bifurcation theory.Numerical simulations are provided to illustrate theoretical discussion.It is observed that Allee effect plays an important role in stability analysis.Strong Allee effect in population enhances the stability of the coexisting steady state.In additional,the effect of fractional-order derivative on dynamic behavior of the system is also investigated.
文摘In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functional response,which is neither differentiable nor locally Lipschitz at the predator axis.This kind of functional response is an extension of the so-called square root functional response,used to model systems in which the prey have a strong herd structure.We study the behavior of the solutions in the first quadrant and the existence of limit cycles.We prove that,for a wide choice of parameters,the solutions arrive at the predator axis in finite time.We also characterize the existence of an equilibrium point and,when it exists,we provide necessary and sufficient conditions for it to be a center-type equilibrium.In fact,we show that the set of parameters that yield a center-type equilibrium,is the graph of a function with an open domain.We also prove that any center-type equilibrium is stable and it always possesses a supercritical Hopf bifurcation.In particular,we guarantee the existence of a unique limit cycle,for small perturbations of the system.
文摘Self-diffusion prerequisite is obtained as the spreading approach of biological populations.Cooperative hunting is a common behavior in predator populations that promotes predation and the coexistence of the prey-predator system.On the other side,the Allee effect among prey may cause the system to become unstable.In this paper,a difusive prey predator system with cooperative hunting and the weak Allee effect in prey populations is discussed.The linear stability and Hopf-bifurcation analysis had been used to examine the system's stability.From the spatial stability of the system,the conditions for Turing instability have been derived.The multiple-scale analysis has been used to derive the amplitude equations of the system.The stability analysis of these amplitude equations leads to the formation of Turing patterns.Finally,numerical simulations are used to analyze spatial patterns forming in 1-D and 2-D.The studies indicate that the model can generate a complex pattern structure and that self-diffusion has a drastic impacton species distribution.
基金Soumitra Pal is thankful to the Council of Scientific and Industrial Research(CSIR),Government of India for providing financial support in the form of senior research fellowship(File No.09/013(0915)/2019-EMR-I).
文摘In this paper,we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population.Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population.The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail.Hopf bifurcation including its direction and stability for the model is also studied.We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system.It is also observed that for a fixed strength of fear,an increase in the Allee parameter makes the system unstable,whereas an increase in prey refuge drives the system toward stability.However,higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction.Further,we explore the variation of densities of the populations in different bi-parameter spaces,where the coexistence equilibrium point remains stable.Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software.
文摘In an environment,the food chains are balanced by the prey-predator interactions.When a predator species is provided with more than one prey population,it avails the option of prey switching between prey species according to their availability.So,prey switching of predators mainly helps to increase the overall growth rate of a predator species.In this work,we have proposed a two prey-one predator system where the predator population adopts switching behavior between two prey species at the time of consumption.Both the prey population exhibit a strong Allee effect and the predator population is considered to be a generalist one.The proposed system is biologically well-defined as the system variables are positive and do not increase abruptly with time.The local stability analysis reveals that all the predator-free equilibria are saddle points whereas the prey-free equilibrium is always stable.The intrinsic growth rates of prey,the strong Allee parameters,and the prey refuge parameters are chosen to be the controlling parameters here.The numerical simulation reveals that in absence of one prey,the other prey refuge parameter can change the system dynamics by forming a stable or unstable limit cycle.Moreover,a situation of bi-stability,tri-stability,or even multi-stability of equilibrium points occurs in this system.As in presence of the switching effect,the predator chooses prey according to their abundance,so,increasing refuge in one prey population decreases the count of the second prey population.It is also observed that the count of predator population reaches a comparatively higher value even if they get one prey population at its fullest quantity and only a portion of other prey species.So,in the scarcity of one prey species,switching to the other prey is beneficial for the growth of the predator population.
基金the Foundation of Education Department of Fujian Province (JAO5204)the Foundation of Science and Technology Department of Fujian Province(2005K027)
文摘In this paper, we study some predator-prey system with Allee effect for prey. In addition, we discuss the properties of equilibrium points and the existence and uniqueness of limit cycle.
基金the National Natural Science Foundation of China (No.1197114312071105)Zhejiang Provincial Natural Science Foundation of China (No.LZ23A010001)。
文摘In this paper, we are concerned with a predator-prey model with Holling type Ⅱ functional response and Allee effect in predator. We first mathematically explore how the Allee effect affects the existence and stability of the positive equilibrium for the system without diffusion. The explicit dependent condition of the existence of the positive equilibrium on the strength of Allee effect is determined. It has been shown that there exist two positive equilibria for some modulate strength of Allee effect. The influence of the strength of the Allee effect on the stability of the coexistence equilibrium corresponding to high predator biomass is completely investigated and the analytically critical values of Hopf bifurcations are theoretically determined.We have shown that there exists stability switches induced by Allee effect. Finally, the diffusion-driven Turing instability, which can not occur for the original system without Allee effect in predator, is explored, and it has been shown that there exists diffusion-driven Turing instability for the case when predator spread slower than prey because of the existence of Allee effect in predator.
文摘Mass production of black soldier fly,Hermetia illucens(L.)(Diptera:Stra-tiomyidae),larvae results in massive heat generation,which impacts facility management,waste conversion,and larval production.We tested daily substrate temperatures with dif-ferent population densities(i.e.,0,500,1000,5000,and 10000 larvae/pan),different pop-ulation sizes(i.e.,166,1000,and 10000 larvae at a fixed feed ratio)and air temperatures(i.e.,20 and 30℃)on various production parameters.Impacts of shifting larvae from 30 to 20℃on either day 9 or 11 were also determined.Larval activity increased substrate tem-peratures significantly(i.e.,at least 10℃above air temperatures).Low air temperature favored growth with the higher population sizes while high temperature favored growth with low population sizes.The greatest average individual larval weights(e.g.,0.126 and 0.124 g)and feed conversion ratios(e.g.,1.92 and 2.08 g/g)were recorded for either 10000 larvae reared at 20℃or 100 larvae reared at 30 C.Shifting temperatures from high(30℃)to low(20℃)in between(~10-d-old larvae)impacted larval production weights(16%increases)and feed conversion ratios(increased 14%).Facilities should consider the impact of larval density,population size,and air temperature during black soldier fly mass production as these factors impact overall larval production.
文摘We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar compet- itive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.
基金This work is jointly supported by the National traditional Medicine Clinical Research Base Business Construction Special Topics(JDZX2015299)the Fundamental Research Funds for the Central University FRF-BR-16-019A.
文摘This paper proposes a diffusive predator-prey model with Allee effect,time delay and anti-predator behavior.First,the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied.Using the normal form and center manifold theory,the formulas which can determine the direction,period and stability of Hopf bifurcation are obtained.Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations,and anti-predator behavior can greatly improve the stability of the coexisting equilibrium.
基金This study is supported by the National Key Research and Development Program of China(2018YFA0801103)the National Natural Science Foundation of China(Grant No.12071330 to Ling Yang,Grant No.11701405 to Jie Yan).
文摘In this paper,we investigate a two-dimensional avian influenza model with Allee effect and stochasticity.We first show that a unique global positive solution always exists to the stochastic system for any positive initial value.Then,under certain conditions,this solution is proved to be stochastically ultimately bounded.Furthermore,by constructing a suitable Lyapunov function,we obtain sufficient conditions for the existence of stationary distribution with ergodicity.The conditions for the extinction of infected avian population are also analytically studied.These theoretical results are conformed by computational simulations.We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model.By scanning different noise intensities,we observe that large noise can cause extinction of infected avian population,which suggests the repression of noise on the spread of avian virus.
基金supported by the Gansu Science and Technology Fund (20JR5RA512)the Research Fund for Humanities and Social Sciences of the Ministry of Education (20XJAZH006)+2 种基金the Fundamental Research Funds for the Central Universities (31920220066)the Gansu Provincial Education Department:Outstanding Postgraduate Innovation Star Project (2023CXZX-196)the Leading Talents Project of State Ethnic Affairs Commission of China and the Innovation Team of Intelligent Computing and Dynamical System Analysis and Application of Northwest Minzu University。
文摘Regarding delay-induced predator-prey models, much research has been done on delayed destabilization, but whether delays are stabilizing or destabilizing is a subtle issue. In this study, we investigate predator-prey dynamics affected by both delays and the Allee effect. We analyze the consequences of delays in different feedback mechanisms. The existence of a Hopf bifurcation is studied, and we calculate the value of the delay that leads to the Hopf bifurcation. Furthermore, applying the normal form theory and a center manifold theorem, we consider the direction and stability of the Hopf bifurcation. Finally, we present numerical experiments that validate our theoretical analysis. Interestingly, depending on the chosen delay mechanism, we find that delays are not necessarily destabilizing. The Allee effect generally increases the stability of the equilibrium, and when the Allee effect involves a delay term, the stabilization effect is more pronounced.
