The dynamics and synchronization of a fractional-order system with complex variables. (English) Zbl 1472.34102

Yang, Xiaoya; Liu, Xiaojun; Dang, Honggang; He, Wansheng

Abstr. Appl. Anal. 2014, Article ID 218537, 8 p. (2014).

Summary: A fractional-order system with complex variables is proposed. Firstly, the dynamics of the system including symmetry, equilibrium points, chaotic attractors, and bifurcations with variation of system parameters and derivative order are studied. The routes leading to chaos including the period-doubling and tangent bifurcations are obtained. Then, based on the stability theory of fractional-order systems, the scheme of synchronization for the fractional-order complex system is presented. By designing appropriate controllers, the synchronization for the system is realized. Numerical simulations are carried out to demonstrate the effectiveness of the proposed scheme.

MSC:

34D06	Synchronization of solutions to ordinary differential equations
34A08	Fractional ordinary differential equations
34H05	Control problems involving ordinary differential equations
34C28	Complex behavior and chaotic systems of ordinary differential equations
34C23	Bifurcation theory for ordinary differential equations

Software:

RODAS

References:

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