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Dynamic properties of the fractional-order logistic equation of complex variables. (English) Zbl 1246.37074

Summary: We study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the continuous dynamical system of the logistic equation of complex variables. The existence and uniqueness of uniformly Lyapunov stable solution will be proved.

MSC:

37F99 Dynamical systems over complex numbers
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D06 Synchronization of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
37M99 Approximation methods and numerical treatment of dynamical systems

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