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Chaotic attractors of the conjugate Lorenz-type system. (English) Zbl 1149.37308
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.
MSC:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)
37G15Bifurcations of limit cycles and periodic orbits
34D08Characteristic and Lyapunov exponents