Hopf bifurcations in an extended Lorenz system

被引：2

作者：

Zhou, Zhiming ^{[1
,2
]}

Tigan, Gheorghe ^{[3
]}

Yu, Zhiheng ^{[4
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China

[2] Hubei Univ Sci & Technol, Dept Math, Wuhan, Hubei, Peoples R China

[3] Politehn Univ Timisoara, Dept Math, Timisoara, Romania

[4] Southwest Jiaotong Univ, Sch Math, Chengdu, Sichuan, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2017年

关键词：

extended Lorenz system; Hopf bifurcation; center manifold; Lyapunov constant; degeneration; ATTRACTORS;

D O I：

10.1186/s13662-017-1083-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we study Hopf bifurcations in the extended Lorenz system, (x) over dot = y, (y) over dot = mx - ny - mxz - px(3), (z) over dot = - az + bx(2), with five parameters m, n, p, a, b. R. For some values of the parameters, this system can be transformed to the classical Lorenz system. In this paper, we give conditions for occurrence of Hopf bifurcation at the equilibrium points. We find totally three limit cycles, each of them located around one of the three equilibria of the system. Numerical simulations illustrate the validity of these conditions and the existence of limit cycles.

引用

页数：10

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