带交错影响的Gray-Scott系统的分岔研究

摘要

The stability and bifurcation situation of Gray-Scott system equilibrium point with cross-diffusion effect is studied by using linear stability method.The results show that the cross-diffusion doesn't affect the equilibrium point, saddle-node bifurcation and Hopf bifurcation characteristics of the system, but affects the Turing bifurcation curve of the system.The results of numerical simulation show that the chaotic degree of wave evolution can be strengthened or weakened by adding staggered effect, which lays a foundation for further model analysis of the system.%采用线性稳定性方法研究了带交错影响的Gray-Scott系统平衡点的稳定性和分岔情况, 结果表明:交错扩散不影响系统的平衡点及鞍结点分岔和霍普夫分岔特性, 但影响系统的图灵分岔线的位置.数值模拟结果显示:加入交错影响还可使系统解波动演化的混乱程度加强或减弱, 为更进一步的系统模式分析奠定了基础.