快慢型超混沌Lorenz系统分析

Analysis of the fast-slow hyperchaotic Lorenz system

讨论了快慢两时间尺度下超混沌Lorenz系统原点的稳定性问题,分析了原点的Hopf分岔,包括Hopf分岔的存在性,分岔方向以及分岔周期解的稳定性等问题,并用数值例子对所得到的结果加以验证.在一定的参数条件下,快慢系统会产生对称簇发并能达到超混沌状态.基于快慢分析法,揭示了对称簇发中沉寂态与激发态相互转迁的不同分岔模式,并进一步分析了耦合强度对慢过效应的影响.

The stability of the origin of the hyperchaotic Lorenz system with two time scales is investigated. The characteristics of Hopf bifurcation from the origin, including the existence condition, the direction as well as the stability of bifurcating periodic solutions are discussed in detail, which can be demonstrated by the numerical simulations. With certain parameter, the fast-slow system can exhibit symmetric bursting and further lead to hyperchaotic movement. Based on the method of slow-fast analysis, different bifurcation forms between quiescent state and spiking has been revealed and the influence of coupling strength on slow passage effect is disscussed.