一类Boissonade模型的稳定性及分支分析

Stability and Bifurcation Analysis in a Kind of Boissonade Model

主要研究了一类刻画化学反应中斑图形成机制的Boissonade模型的动力学行为。首先,研究了该系统的正平衡解的存在性。其次,研究了系统的零平衡解及正平衡解的稳定性和系统的正平衡解附近的Hopf分支的存在性问题。最后,研究了平衡解的性质并给出了参数平面分支图。

In this paper, a kind of Boissonade model describing the formation of Turing patterns is investigated. Firstly, we consider the existence of the positiveequilibrium solution. Secondly, we study the stability of the nonnegative equilibriumsolutions and the ex- istence of Hopf bifurcation near the positive equilibrium solution. Finally, we investigate the property of the equilibrium solution and provide bifurcation diagram in the parameter plane.