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Lü, Jinhu; Chen, Guanrong; Cheng, Daizhan

A new chaotic system and beyond: the generalized Lorenz-like system. (English) Zbl 1129.37323

Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 5, 1507-1537 (2004).
Summary: This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-scroll chaotic attractor or confine two attractors to a 2-scroll chaotic attractor under the control of a simple constant input. Furthermore, the concept of generalized Lorenz system is extended to a new class of generalized Lorenz-like systems in a canonical form. Finally, the important problems of classification and normal form of three-dimensional quadratic autonomous chaotic systems are formulated and discussed.

Cited in 2 Reviews
Cited in 126 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C28 Complex behavior and chaotic systems of ordinary differential equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure

Keywords:

Multi-scroll chaotic attractor; chaotification; three-dimensional quadratic autonomous system; Lorenz-like system; normal form
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\textit{J. Lü} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 5, 1507--1537 (2004; Zbl 1129.37323)
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