一类具有时滞的 Gierer-Meinhardt 活化抑制模型的分支分析

摘要/Abstract

摘要：

该文研究了一类在齐次 Neumann 边界条件下具有时滞扩散的 Gierer-Meinhardt 活化抑制模型. 首先, 利用谱理论得到了该模型正平衡点的局部渐近稳定性; 其次, 以时滞为分支参数, 研究了该模型 Hopf 分支的存在性; 接着, 根据偏泛函微分方程的中心流形定理和正规型理论, 得到了该 Hopf 分支方向和分支周期解的稳定性; 最后, 利用 Matlab 软件, 模拟了该系统在临界点附近经历的 Hopf 分支.

关键词: 时滞, Gierer-Meinhardt 模型, Hopf 分支, 稳定性, 数值模拟

Abstract:

In this paper, we consider a class of Gierer-Meinhardt activation inhibition model with time delay diffusion under homogeneous Neumann boundary conditions. Firstly, the local asymptotic stability of the positive equilibrium of the model is obtained by using spectral theory; second, choosing the time delay as the bifurcation parameter, the existence of the Hopf bifurcation of the model is analyzed; next, the formulae to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions by applying the center manifold theorem and normal form theory for partial differential equation are derived; finally, numerical simulations are also carried out to simulate the Hopf bifurcation that the model go through near the critical point.

Key words: Time delay, Gierer-Meinhardt model, Hopf bifurcation, Stability, Simulation

中图分类号:

O175.12

马亚妮, 袁海龙. 一类具有时滞的 Gierer-Meinhardt 活化抑制模型的分支分析[J]. 数学物理学报, 2023, 43(6): 1774-1788.

Ma Yani, Yuan Hailong. Bifurcation Analysis of a Class of Gierer-Meinhardt Activation Inhibition Model with Time Delay[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1774-1788.

图/表 6

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