Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria. (English) Zbl 1213.37061

Wei, Zhouchao; Yang, Qigui

Nonlinear Anal., Real World Appl. 12, No. 1, 106-118 (2011).

The authors introduce a new chaotic system described by a system of three ordinary differential equations with six terms, one of which is nonlinear (exponential function). They study its properties with the goal to compare the topological structure of a new system with that of a Lorenz system and some other known Lorenz-like chaotic systems. The existence of singularly degenerate heteroclinic cycles, periodic solutions and chaotic attractors are investigated. It is shown that in the case when all equilibria of a new system are stable, the system gives rise to a double-scroll chaotic attractor which does not satisfy the conditions of the Sil’nikov homoclinic theorem. The results of numerical simulations are also provided.

Reviewer: Yuri V. Rogovchenko (Umeå)

MSC:

37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28	Complex behavior and chaotic systems of ordinary differential equations

Keywords:

chaotic system; attractor; Lyapunov exponents; Poincaré map; degenerate heteroclinic cycle

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