具有集群行为的捕食者-食饵反应扩散系统的稳定性和Turing不稳定性

Stability and Turing instability of a predator-prey reaction-diffusion system with schooling behavior

考虑了具有集群行为的鱼群捕食者-食饵反应扩散系统。通过详细分析系统在唯一正常数平衡解处线性化系统的特征方程的根在复平面上的分布情况,讨论系统唯一正常数平衡解的局部渐近稳定性以及Turing不稳定性,并且利用MATLAB软件对所获得的理论结论进行了数值验证。

A predator-prey reaction-diffusion system of fish with schooling behavior is considered. By analyzing the distribution of the roots of the characteristic equation of the linearized system at the unique constant positive equilibrium solution in the complex plane in detail, the stability and the Turing instability of the unique positive equilibrium solution of the system are discussed. In addition, the obtained theoretical conclusions are verified numerically by MATLAB software.