Positive Steady State Solutions of a Diffusive Leslie-gower Predator-prey Model with Holling Type Ii Functional Response and Cross-diffusion
نویسندگان
چکیده
In this paper we consider a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion under zero Dirichlet boundary condition. By using topological degree theory, bifurcation theory, energy estimates and asymptotic behavior analysis, we prove the existence, uniqueness and multiplicity of positive steady states solutions under certain conditions on the parameters.
منابع مشابه
Global stability and stationary pattern of a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response
This paper is concerned with a diffusive prey-predator model with modified Leslie-Gower term and Holling II functional response subject to the homogeneous Neumann boundary condition. Firstly, by upper and lower solutions method, we prove the global asymptotic stability of the unique positive constant steady state solution. Secondly, introducing the cross diffusion, we obtain the existence of no...
متن کاملPositive periodic solutions for a predator-prey model with modified Leslie-Gower Holling-type II schemes and a deviating argument
In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model. Keywords— Predator-prey model, Holling II type functional response, Positive periodic solution, Coincidence degree theorem
متن کاملWave Analysis of a Diffusive Modified Leslie-Gower Predator-prey System with Holling Type IV Schemes
A diffusive predator-prey model with modified Leslie-Gower and Holling type IV schemes is investigated analytically and numerically. Mathematical theoretical works mainly focus on the existence of traveling wave solutions. Numerical simulations are performed to confirm the feasibility of traveling wave solutions. All these results are significant in exploration of the dynamic complexity of ecos...
متن کاملThe existence, bifurcation and stability of positive stationary solutions of a diffusive LeslieGower predatorprey model with Holling-type II functional responses
In this paper, we revisit a diffusive Leslie–Gower predator–preymodel with Holling-type II functional responses and Dirichlet boundary condition. It is shown that multiple positive steady state solutions exist under certain conditions on the parameters, while for another parameter region, the positive steady state solution is unique and locally asymptotically stable. Results are proved by using...
متن کاملOn existence, multiplicity, uniqueness and stability of positive solutions of a Leslie–Gower type diffusive predator–prey system
where u and v, respectively, represent the populations of the prey and the predator, and r, s, K, h are positive constants. The prey grows logistically with carrying capacity K and intrinsic growth rate r in the absence of predation. The predator consumes the prey according to the functional response f(u) and grows logistically with intrinsic growth rate s. The carrying capacity of the predator...
متن کامل