The spatially inhomogeneous Hopf bifurcation induced by memory delay in a memory-based diffusion system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:300

Article

Song, Yongli¹  Peng, Yahong²  Zhang, Tonghua³ 

[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China

[2] Donghua Univ, Dept Math, Shanghai 201620, Peoples R China

[3] Swinburne Univ Technol, Dept Math, Hawthorn, Vic 3122, Australia

关键词: Spatial memory;    Delay;    Hopf bifurcation;    Normal form;    Periodic solution;   

DOI  :  10.1016/j.jde.2021.08.010

来源: Elsevier

【 摘 要 】

The memory-based diffusion systems have wide applications in practice. Hopf bifurcations are observed from such systems. To meet the demand for computing the normal forms of the Hopf bifurcations of such systems, we develop an effective new algorithm where the memory delay is treated as the perturbation parameter. To illustrate the effectiveness of the algorithm, we consider a diffusive predator-prey system with memory-based diffusion and Holling type-II functional response. By employing this newly developed procedure, we investigate the direction and stability of the delay-induced mode-1 and mode-2 Hopf bifurcations. Numerical simulations confirm our theoretical findings, that is the existence of stable spatially inhomogeneous periodic solutions with mode-1 and mode-2 spatial patterns, and the transition from the unstable mode-2 spatially inhomogeneous periodic solution to the stable mode-1 spatially inhomogeneous periodic solution. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free