Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response  

作　　者：Dong Wang Yani Ma Dong Wang;Yani Ma(College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China)

机构地区：[1]College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第6期2190-2211,共22页应用数学与应用物理（英文）

摘　　要：In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

关 键 词：Modified Leslie-Gower Model Crowley-Martin Function Response Hopf Bifurcation Transcritical Bifurcation Turing Instability 

分 类 号：O17[理学—数学]