具有饱和效应的任意阶自催化反应扩散模型的Turing不稳定性和Hopf分支

利用Hopf分支理论，研究一类具有饱和效应的任意阶自催化反应扩散模型.首先，对常微分系统给出正平衡点的稳定性，且以a为分支参数给出Hopf分支的存在性及稳定性；其次，对扩散系统建立由扩散引起的Turing不稳定性，同时给出Hopf分支的存在性；最后，用数值模拟实例验证理论分析结果的正确性.

Turing Instability and Hopf Bifurcation for Arbitrary Order Autocatalysis Reaction-Diffusion Model with Saturation Effect

By using the Hopf bifurcation theory, we studied an arbitrary order autocatalysis reaction-diffusion model with saturation effect. Firstly, the stability of the positive equilibrium points for the ordinary differential system was given, and the existence and stability of Hopf bifurcation were given by taking a as the bifurcation parameter. Secondly, the Turing instability caused by  diffusion was established for diffusion system, and the existence of Hopf bifurcation was given. Finally, some numerical simulation examples were used to verify the correctness of the theoretical analysis results.