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Yang, Qigui; Chen, Guangrong; Huang, Kuifei

Chaotic attractors of the conjugate Lorenz-type system. (English) Zbl 1149.37308

Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 3929-3949 (2007).
A new conjugate Lorenz-type system is introduced in this paper. The system contains as special cases the conjugate Lorenz system, conjugate Chen system and conjugate Lü system. Chaotic dynamics of the system in the parametric space is numerically and thoroughly investigated. Meanwhile, a set of conditions for possible existence of chaos are derived, which provide some useful guidelines for searching chaos in numerical simulations. Furthermore, some basic dynamical properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions and the compound structure of the system are demonstrated with various numerical examples.

Cited in 33 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34D08 Characteristic and Lyapunov exponents of ordinary differential equations

Keywords:

chaos; conjugate Lorenz-type system; Hopf bifurcation; Lyapunov exponent; Lorenz system; Chen system; Lü system
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\textit{Q. Yang} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 3929--3949 (2007; Zbl 1149.37308)
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