Gierer-Meinhardt模型的稳定分析和时空分歧

Stability analysis and spatially bifurcation for a Gierer-Meinhardt model

在齐次Neumann边界条件下,讨论了Gierer-Meinhardt模型的稳态分歧和Hopf分歧.给出了正常数解的稳定性.利用分歧理论、空间分解和隐函数定理研究了系统的单重和二重分歧,并且以d2为分歧参数考察了系统的Hopf分歧,得到了非齐次周期解存在的条件.

The steady-states bifurcations and Hopf bifurcation for a Gierer-Meinhardt model with homogeneous Neumann boundary conditions are considered. The stability of the positive constant solution is discussed. Furthermore, the bifurcations from simple and double eigenvalues are investigated by means of the combination of the simple bifurcation theory, space decomposition and implicit function theorem. Finally, by regarding d2 as a bifurcation parameter, we study the Hopf bifurcation and obtain the conditions of the existence of inhomogeneous periodic solution.