Dynamical analysis of a new fractional-order Rabinovich system and its fractional matrix projective synchronization |
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Authors: | Jinman He Fangqi Chen |
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Institution: | 1. Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China |
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Abstract: | This paper constructs a new physical system, i.e., the fractional-order Rabinovich system, and investigates its stability, chaotic behaviors, chaotic control and matrix projective synchronization. Firstly, two Lemmas of the new system's stability at three equilibrium points are given and proved. Next, the largest Lyapunov exponent, the corresponding bifurcation diagram and the chaotic behaviors are studied. Then, the linear and nonlinear feedback controllers are designed to realize the system's local asymptotical stability and the global asymptotical stability, respectively. It's particularly significant that, the fractional matrix projective synchronization between two Rabinovich systems is achieved and two kinds of proofs are provided for Theorem 4.1. Especially, under certain degenerative conditions, the fractional matrix projective synchronization can be reduced to the complete synchronization, anti-synchronization, projective synchronization and modified projective synchronization of the fractional-order Rabinovich systems. Finally, all the theoretical analysis is verified by numerical simulation. |
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Keywords: | Fractional-order Rabinovich system Chaotic attractors Chaotic control Fractional matrix projective synchronization |
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