Analysis of the fast-slow hyperchaotic Lorenz system
快慢型超混沌Lorenz系统分析

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.