一个具有唯一鞍焦点的三维混沌系统分析

讨论了一个具有唯一鞍焦点的多参数三维混沌系统,该系统包含了Sprott提出的一个最简混沌模型.在特定的条件下得到了Hopf分岔的存在性条件;进一步利用规范型理论获得了决定Hopf分岔方向和分支周期解稳定性的公式,同时利用计算机模拟证实本文的理论分析结果.

Analysis of a 3D Chaotic System with Only One Saddle Foci Equilibrium

In this paper,a 3D chaotic system with multi-parameters and only one saddle foci equilibrium is investigated,which contains one of the simplest systems construsted by Sprott.We prove the existence of the Hopf bifurcation under some particular conditions. By means of normal form theory,we obtain a formula for determining the direction of the Hopf bifurcation and the stability of bifurcating period solutions.Meanwhile,numerical simulations are performed to justify theoretical analysis.