Affiliation:
1. School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China
Abstract
<p style='text-indent:20px;'>In this paper, we consider a predator-prey model with memory-based diffusion. We first analyze the stability of all steady states in detail. Then by analyzing the distribution of eigenvalues, we find that the average memory period can cause the stability change of the positive steady state, and Hopf bifurcation occurs at the positive steady state. Moreover, from the central manifold theorem and the normal form theory, we give the direction and stability of Hopf bifurcation. The results show that, under certain conditions, a family of spatially inhomogeneous periodic solutions will bifurcate from the positive steady state when the average memory period appear.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
Reference42 articles.
1. F. B. M. Belgacem, C. Cosner.The effect of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canad. Appl. Math. Quart., 3 (1995), 379-397.
2. S. Busenberg, W. Huang.Stability and Hopf bifurcation for a population delay model with diffusion effects, J. Differential Equations, 124 (1996), 80-107.
3. R. S. Cantrell, C. Cosner.On the dynamics of predator-prey models with the Beddington-DeAngelis functional response, J. Math. Anal. Appl., 257 (2001), 206-222.
4. S. Chen, Y. Lou, J. Wei.Hopf bifurcation in a delayed reaction-diffusion-advection population model, J. Differential Equations, 264 (2018), 5333-5359.
5. S. S. Chen, J. P. Shi.Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect, J. Differential Equations, 253 (2012), 3440-3470.
Cited by
18 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献