时滞Lengyel-Epstein反应扩散系统的Hopf分支  

Hopf bifurcation analysis in the Lengyel-Epstein reaction diffusion system with time delay

作　　者：王雅迪 袁海龙 WANG Yadi;YUAN Hailong(School of Mathematics&Data Science,Shaanxi University of Science&Technology,Xi'an 710021,Shaanxi,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《山东大学学报（理学版）》2023年第8期92-103,共12页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11901370);陕西省自然科学基础研究计划资助项目(2019JQ-516);陕西省教育厅专项科研计划资助项目(19JK0142)。

摘　　要：在齐次Neumann边界条件下,研究具有时滞延迟效应的Lengyel-Epstein反应扩散系统。首先,以时滞参数作为分支参数,研究时滞效应对该系统正常数平衡点稳定性的影响,并得到产生Hopf分支的条件;其次,利用偏泛函微分方程的规范型理论和中心流形定理,给出Hopf分支方向和分支周期解的稳定性;最后,借助MATLAB软件进行数值模拟,验证结论。The Lengyel-Epstein reaction diffusion system with time delay subject to Neumann boundary conditions is considered.By choosing the time delay as the bifurcation parameter,the stability/instability of the unique positive constant equilibrium and the existence of Hopf bifurcation are investigated.In addition,the formulae to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by applying the normal form theory and center manifold theorem for partial differential equation are derived.Finally,some numerical simulations are carried out to support the analytical results.

关 键 词：HOPF分支 时滞 Lengyel-Epstein系统 稳定性 数值模拟 

分 类 号：O175.12[理学—数学]