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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.

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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