Dynamical analysis of the generalized Sprott C system with only two stable equilibria. (English) Zbl 1252.93067

Wei, Zhouchao; Yang, Qigui

Nonlinear Dyn. 68, No. 4, 543-554 (2012).

Summary: A generalized Sprott C system with only two stable equilibria is investigated by detailed theoretical analysis as well as dynamic simulation, including some basic dynamical properties, Lyapunov exponent spectra, fractal dimension, bifurcations, and routes to chaos. In the parameter space where the equilibria of the system are both asymptotically stable, chaotic attractors coexist with period attractors and stable equilibria. Moreover, the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters is investigated. Periodic solutions and chaotic attractors can be found when these cycles disappear.

MSC:

93C15	Control/observation systems governed by ordinary differential equations
37N35	Dynamical systems in control
34H10	Chaos control for problems involving ordinary differential equations
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

chaotic attractors; degenerate heteroclinic cycles; Sil’nikov theorem; Lyapunov exponent; coexisting attractors

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