HOMOCLINIC AND HETEROCLINIC ORBITS AND BIFURCATIONS OF A NEW LORENZ-TYPE SYSTEM

作者：Li, Xianyi^*; Wang, Haijun

来源：International Journal of Bifurcation and Chaos, 2011, 21(9): 2695-2712.

DOI：10.1142/S0218127411030039

• Lorenz-type system
• center manifold theorem
• degenerate pitchfork bifurcation
• Hopf bifurcation
• homoclinic and heteroclinic orbit

In this paper, a new Lorenz-type system with chaotic attractor is formulated. The structure of the chaotic attractor in this new system is found to be completely different from that in the Lorenz system or the Chen system or the Lu system, etc., which motivates us to further study in detail its complicated dynamical behaviors, such as the number of its equilibrium, the stability of the hyperbolic and nonhyperbolic equilibrium, the degenerate pitchfork bifurcation, the Hopf bifurcation and the local manifold character, etc., when its parameters vary in their space. The existence or nonexistence of homoclinic and heteroclinic orbits of this system is also rigorously proved. Numerical simulation evidences are also presented to examine the corresponding theoretical analytical results.

• 出版日期2011-9
• 单位深圳大学