一个三维系统的音叉分岔

Pitchfork bifurcations of a three-dimensional system

摘要:

本文研究了一个三维系统的音叉分岔.该系统中的每个方程都包含一个二次交叉乘积项. 本文分析了当单个参数在临界值附近变化时系统的平衡点数量的改变, 即单个参数的音叉分歧, 以及系统发生音叉分岔时产生的平衡点的稳定性.

Abstract:

This paper aims at the pitchfork bifurcations of a three-dimensional system, in which each equation of the system contains a single quadratic cross-product term. The change of the number of equilibria of the system as one parameter varies near a critical value, i.e., the pitchfork bifurcations for one parameter, is analyzed. The stability of the equilibria generated by the pitchfork bifurcations is investigated as well.