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....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.展开更多
In this paper, we consider a diffusive density-dependent predator-prey model with Crowley-Martin functional responses subject to Neumann boundary condition. We ana- lyze the stability of the positive equilibrium and t...In this paper, we consider a diffusive density-dependent predator-prey model with Crowley-Martin functional responses subject to Neumann boundary condition. We ana- lyze the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through the distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally, numerical simulations are given to verify our theoretical analysis.展开更多
文摘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.
文摘In this paper, we consider a diffusive density-dependent predator-prey model with Crowley-Martin functional responses subject to Neumann boundary condition. We ana- lyze the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through the distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally, numerical simulations are given to verify our theoretical analysis.
基金Supported by National Natural Science Foundation of China(1127104511261041)+1 种基金Natural Science Foundation of Ningxia University(NDZR1301)Startup Foundation for Doctor Scientific Research of Ningxia University
