Bridge the gap between the Lorenz system and the Chen system. (English) Zbl 1043.37026

Lü, Jinhu; Chen, Guanrong; Cheng, Daizhan; Celikovsky, Sergej

Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 12, 2917-2926 (2002).

Summary: This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

MSC:

37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28	Complex behavior and chaotic systems of ordinary differential equations
37N05	Dynamical systems in classical and celestial mechanics
70Q05	Control of mechanical systems
93B52	Feedback control

Keywords:

Lorenz system; Chen system; critical system; unified chaotic system; controlling the Duffing oscillator; numerical simulations; attractors; bifurcations

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