一类四维动力系统孤立奇点稳定性分析

Stability Analysis of Isolated Equilibrium for a Class of 4-D Dynamic Systems

考虑一类反应扩散方程在常稳态意义下转化为四维动力系统,从线性化特征值方法入手,分析讨论了Hamilton系统条件下的各种临界情形,并把系统的奇点稳定性与Hamilton函数的极值情况相对应,运用极值判别法和构造流形的方法给出了不同类型非线性系统孤立奇点稳定性的判据.

A class of 4-dimensional dynamic systems converted from a steady state of a class of reaction-diffusion systems is studied. Various critical cases under a Hamiltonian system are analyzed via a linearization technique and eigenvalues of the linearization matrix. A link between a stability analysis on equilibrium of dynamic systems and the extreme of Hamilton function is applied. Methods for extreme discrimination and manifold construction are adapted to consider the stability of isolated equilibrium of different types of nonlinear dynamic systems