Abstract
This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.
Highlights
The history of fractional calculus is more than three centuries old
This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system
Many authors began to investigate the chaotic dynamics of fractional-order nonlinear systems with the help of fractional calculus
Summary
The history of fractional calculus is more than three centuries old. It has been found that the behavior of many physical systems can be properly described by fractional-order systems, for example, dielectric polarization, electrode-electrolyte polarization, electromagnetic waves, viscoelastic systems, quantitative finance, and diffusion waves 1–3. Based on the idea of a nonlinear observer, Peng and Jiang proposed a new method and applied it to generalized projective synchronization for a class of fractional-order chaotic systems ; Wu and Wang discussed a new fractional-order system and investigated its projective synchronization by designing the suitable nonlinear controller. The antisynchronization of two identical and two nonidentical hyperchaotic fractional-order systems is investigated via sliding mode controller in , but the results about the projective synchronization and inverse synchronization are relatively few. Wu and Lu investigated the generalized projective synchronization of fractional-order Chen hyperchaotic systems 12. Motivated by the above discussions, in this letter, we study the inverse projective synchronization between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system.
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