具Logistic增长项的极小趋化系统的稳定性分析

Stability analysis of a minimal chemotaxis model with logistic growth

利用扰动分析给出极小趋化系统的线性化系统,然后通过分析各个模态的振幅的长时间行为给出常数定态解的稳定性分析.发现平凡定态解总是不稳定,非平凡常数定态解的稳定性依赖于趋化系数,即当趋敏效应较强时,所有常数定态解都不稳定,从而预测了非常数定态解的存在性.最后结合数值实例,验证了理论分析的结果,且预测了非常数定态解的稳定性.

Using perturbation analysis we obtained the linearized system of the minimal chemotaxis system. Then we analyzed the stability of constant steady-state solutions by studying the long-time behavior of the amplitude of each mode. It was found that the trivial solution was unstable and the non-trivial constant solution chemotactic coefficient played the key role. When the chemotactic effect was stronger, all constant solutions were unstable. It suggested the existence of non-constant steady state solutions. Finally, numerical examples testified the theoretical results and predicted the stability of non constant steady-state solutions.