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Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems. (English) Zbl 1215.37024
Summary: Recently, the fractional-order Chen-Lee system was proven to exhibit chaos by the presence of a positive Lyapunov exponent. However, the existence of chaos in fractional-order Chen-Lee systems has never been theoretically proven in the literature. Moreover, synchronization of chaotic fractional-order systems was extensively studied through numerical simulations in some of the literature, but a theoretical analysis is still lacking. Therefore, we devoted ourselves to investigating the theoretical basis of chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems in this paper. Based on the stability theorems of fractional-order systems, the necessary conditions for the existence of chaos and the controllers for hybrid projective synchronization were derived. The numerical simulations show coincidence with the theoretical results.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34A08 Fractional ordinary differential equations and fractional differential inclusions
34D20 Stability of solutions to ordinary differential equations
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