Dynamical properties and simulation of a new Lorenz-like chaotic system

作者：Li, Xianyi^*; Ou, Qianjun

来源：Nonlinear Dynamics, 2011, 65(3): 255-270.

DOI：10.1007/s11071-010-9887-z

• Lorenz-type system
• Center Manifold Theorem
• Pitchfork bifurcation
• Hopf bifurcation
• Homoclinic and heteroclinic orbit

This paper formulates a new three-dimensional chaotic system that originates from the Lorenz system, which is different from the known Lorenz system, Rossler system, Chen system, and includes Lu systems as its special case. By using the center manifold theorem, the stability character of its non-hyperbolic equilibria is obtained. The Hopf bifurcation and the degenerate pitchfork bifurcation, the local character of stable manifold and unstable manifold, are also in detail shown when the parameters of this system vary in the space of parameters. Corresponding bifurcation cases are illustrated by numerical simulations, too. The existence or non-existence of homoclinic and heteroclinic orbits of this system is also studied by both rigorous theoretical analysis and numerical simulation.

• 出版日期2011-8
• 单位深圳大学