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Chaos in fractional conjugate Lorenz system and its scaling attractors. (English) Zbl 1222.37037

Summary: Chaotic dynamics of fractional conjugate Lorenz systems are demonstrated in terms of local stability and largest Lyapunov exponent. Chaos does exist in the fractional conjugate Lorenz system with order less than three since it has positive largest Lyapunov exponent. Furthermore, scaling chaotic attractors of a fractional conjugate Lorenz system is theoretically and numerically analyzed with the help of a one-way synchronization method and an adaptive synchronization method. Numerical simulations are performed to verify the theoretical analysis.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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