A New Chaotic System and Beyond: the Generalized Lorenz-like System

By Jinhu Lu, Guanrong Chen, DaiZhan Cheng. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2004

317 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/03408be67f6c21cf9035390be6f9a738234679b2

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Citations in the corpus

New results on stability and stabilization of a class of nonlinear fractional-order systems (2013, background): “The so-called Lü system is known as a bridge between the Lorenz system and Chen system [29].”
Generating multiscroll Chaotic attractors: Theories, Methods and Applications (2006, methodology): “It should be pointed out that one can construct the rigorously mathematical formulation for this map by using an exact solution, as given in [Lü et al., 2004d].”
Chaos synchronization of a chaotic system via nonlinear control (2005, background): “[21] and display two chaotic attractors simultaneously: _ x 1⁄4 ab aþb x yzþ c; _ y 1⁄4 ay þ xz; _ z 1⁄4 bzþ xy; (8)>< >: ð1Þ”