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A unified Lorenz-type system and its canonical form. (English) Zbl 1185.37088
Summary: Based on the generalized Lorenz system, a conjugate Lorenz-type system is introduced, and a new unified Lorenz-type system containing these two classes of systems is naturally constructed in the paper. Such a unified system is state-equivalent to a simple special form, which is parameterized by two parameters that are useful for tuning of chaotic behavior and system classification. More importantly, based on the parameterized form, three new chaotic attractors, called conjugate attractors, are found for the first time. They are conjugate to the Lorenz attractor, the Chen attractor, and the Lü attractor, respectively.
MSC:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)