This paper investigates the global dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey model in open advective environments.We find that there exist critical advection rates,intrinsic growth rates,di...This paper investigates the global dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey model in open advective environments.We find that there exist critical advection rates,intrinsic growth rates,diffusion rates and length of the domain,which classify the global dynamics of the Leslie-Gower predator-prey system into three scenarios:coexistence,persistence of prey only and extinction of both species.The results reveal some significant differences with the classical specialist and generalist predator-prey systems.In particular,it is found that the critical advection rates of prey and predator are independent of each other and the parameters about predation rate have no influence on the dynamics of system.The theoretical results provide some interesting highlights in ecological protection in streams or rivers.展开更多
A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of s...A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of sufcient conditions which guarantee the persistent property and global attractivity of the system is obtained. Also, by applying the comparison theorem of diferential equations and Fluctuation Lemma, a set of sufcient conditions which ensure the extinction of the prey species and the global attractivity of predator species is obtained. This result shows that for the Lotka-Volterra type predator-prey system, when the value of prey refuge increases, predator species will be driven to extinction due to the lack of food. Our study shows that the alternative food resource predator species is always permanent, which means that prey refuge has no infuence on the permanence of predator species. However, refuge plays an important role in the persistent property of the prey species: large enough prey refuge could keep the persistent property of the prey species, while small enough refuge could lead to the extinction of prey species. Numerical simulations show the feasibility of the main results.展开更多
基金supported by the National Natural Science Foundation of China(11871403)Fundamental Research Funds for the Central Universities(XDJK2020B050).
文摘This paper investigates the global dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey model in open advective environments.We find that there exist critical advection rates,intrinsic growth rates,diffusion rates and length of the domain,which classify the global dynamics of the Leslie-Gower predator-prey system into three scenarios:coexistence,persistence of prey only and extinction of both species.The results reveal some significant differences with the classical specialist and generalist predator-prey systems.In particular,it is found that the critical advection rates of prey and predator are independent of each other and the parameters about predation rate have no influence on the dynamics of system.The theoretical results provide some interesting highlights in ecological protection in streams or rivers.
文摘A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of sufcient conditions which guarantee the persistent property and global attractivity of the system is obtained. Also, by applying the comparison theorem of diferential equations and Fluctuation Lemma, a set of sufcient conditions which ensure the extinction of the prey species and the global attractivity of predator species is obtained. This result shows that for the Lotka-Volterra type predator-prey system, when the value of prey refuge increases, predator species will be driven to extinction due to the lack of food. Our study shows that the alternative food resource predator species is always permanent, which means that prey refuge has no infuence on the permanence of predator species. However, refuge plays an important role in the persistent property of the prey species: large enough prey refuge could keep the persistent property of the prey species, while small enough refuge could lead to the extinction of prey species. Numerical simulations show the feasibility of the main results.
