By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) period...By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.展开更多
In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions ...In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference-differential equations.展开更多
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive...A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.展开更多
Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and s...Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and stability of pest eradication periodic solution are provided under the assumptions of releasing natural enemies either more or less frequent than spray. In order to address how the different pulse time points, control tactics affect the pest control （i.e. the threshold value）, the Holling Type II Lotka-Volterra predator- prey system, as an example, with impulsive intervention at different time points axe investigated carefully. The numerical results show how the threshold values are affected by the factors including instantaneous killing rates of pesticides on pests and natural enemies, the release rate of natural enemies and release constant, timing of pesticide application and timing of release period. Furthermore, it is confirmed that the system has the coexistences of pests and natural enemies for a wide range of parameters and with quite different pest amplitudes.展开更多
In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of pos...In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.展开更多
The paper analyzes the equity of road resources distribution in urban areas by modeling the competitive relationship among different road users. A logistic model is used to describe the development of different traffi...The paper analyzes the equity of road resources distribution in urban areas by modeling the competitive relationship among different road users. A logistic model is used to describe the development of different traffic modes in the transportation network. The system is similar to the species competition model, so a two-species model is used to analyze the relationship between users based on the stability of the equilibrium points. The Lotka-Volterra model is then used to describe the multi-species cases with numerical examples, showing that this model can describe the effects of the road space distribution on the competitive user relationships. Policy makers must ensure the equity of road resources distribution so that each urban transportation mode is properly developed for sustainable social development.展开更多
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Ho...We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.展开更多
<正> By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show t...<正> By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show that the locally asymptotical stable equilibrium point of Lotka-Volterra food chain systems for 7 dimension must be globally stable.展开更多
The competition and dynamics of dominant trees species in the forest ecotone between the broad-leaved/Korean pine （Pinus koraiensis） mixed forest and the spruce-fir forest （also known as dark conifer forest） in Ch...The competition and dynamics of dominant trees species in the forest ecotone between the broad-leaved/Korean pine （Pinus koraiensis） mixed forest and the spruce-fir forest （also known as dark conifer forest） in Changbai Mountain, Jilin Province in Northeast China were studied by using Lotka-Volterra model, based on the data from twenty-eight sample plots with area of 20 mx90 m for each one. Results showed that under natural condition, differentiation of communities followed two directions： one would be Spruce （Picea jezoensis and few P. koraiensis） and fir （Abies nephrolepis） co-dominant conifer forest, and at the equilibrium fir was absolutely preponderant （77.1% of relative dominance （RD））; the other would be the conifer and broad-leaved mixed forest, and at equilibrium, the broad-leaved tree species was 50% of RD in the broad-leaved/Korean pine mixed forest and 66% of RD in the broad-leaved and spruce-fir mixed forest. The study demonstrated that both broad-leaved/Korean pine mixed forest and dark conifer forest were climax community, the ecotone had transitional characteristics, and the diversification of the forest communities suggested that the direction of succession was affected by local habitat.展开更多
In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternativ...In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.展开更多
文摘By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.
文摘In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference-differential equations.
文摘A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
文摘Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and stability of pest eradication periodic solution are provided under the assumptions of releasing natural enemies either more or less frequent than spray. In order to address how the different pulse time points, control tactics affect the pest control （i.e. the threshold value）, the Holling Type II Lotka-Volterra predator- prey system, as an example, with impulsive intervention at different time points axe investigated carefully. The numerical results show how the threshold values are affected by the factors including instantaneous killing rates of pesticides on pests and natural enemies, the release rate of natural enemies and release constant, timing of pesticide application and timing of release period. Furthermore, it is confirmed that the system has the coexistences of pests and natural enemies for a wide range of parameters and with quite different pest amplitudes.
基金supported by the National Natural Science Foundation of China under Grant No.11302002the Foundation of Outstanding Young Talent in University of Anhui Province of China under Grant No.2011SQRL022ZD
文摘In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.
基金the National Natural Science Foundation of China (No. 70571046)
文摘The paper analyzes the equity of road resources distribution in urban areas by modeling the competitive relationship among different road users. A logistic model is used to describe the development of different traffic modes in the transportation network. The system is similar to the species competition model, so a two-species model is used to analyze the relationship between users based on the stability of the equilibrium points. The Lotka-Volterra model is then used to describe the multi-species cases with numerical examples, showing that this model can describe the effects of the road space distribution on the competitive user relationships. Policy makers must ensure the equity of road resources distribution so that each urban transportation mode is properly developed for sustainable social development.
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
基金supported by National Natural Science Foundation of China(Grant No.11201380)the Fundamental Research Funds for the Central Universities(Grant No.XDJK2012B007)+2 种基金Doctor Fund of Southwest University(Grant No.SWU111021)Educational Fund of Southwest University(Grant No.2010JY053)National Research Foundation of Korea Grant funded by the Korean Government(Ministry of Education,Science and Technology)(Grant No.NRF-2011-357-C00006)
文摘We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.
基金Project supported by the National Natural Science Foundation of China.
文摘<正> By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show that the locally asymptotical stable equilibrium point of Lotka-Volterra food chain systems for 7 dimension must be globally stable.
基金This research was supported by Ph.D. Startup Funding and Overseas Scholar Funding from Institute of Applied Ecology, Chinese Academy of Sciences and funding from Opened Research Station of Changbai Mountain Forest Ecosystems.
文摘The competition and dynamics of dominant trees species in the forest ecotone between the broad-leaved/Korean pine （Pinus koraiensis） mixed forest and the spruce-fir forest （also known as dark conifer forest） in Changbai Mountain, Jilin Province in Northeast China were studied by using Lotka-Volterra model, based on the data from twenty-eight sample plots with area of 20 mx90 m for each one. Results showed that under natural condition, differentiation of communities followed two directions： one would be Spruce （Picea jezoensis and few P. koraiensis） and fir （Abies nephrolepis） co-dominant conifer forest, and at the equilibrium fir was absolutely preponderant （77.1% of relative dominance （RD））; the other would be the conifer and broad-leaved mixed forest, and at equilibrium, the broad-leaved tree species was 50% of RD in the broad-leaved/Korean pine mixed forest and 66% of RD in the broad-leaved and spruce-fir mixed forest. The study demonstrated that both broad-leaved/Korean pine mixed forest and dark conifer forest were climax community, the ecotone had transitional characteristics, and the diversification of the forest communities suggested that the direction of succession was affected by local habitat.
文摘In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.
