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A new fractional-order jerk system and its hybrid synchronization. (English) Zbl 1408.34015

Azar, Ahmad Taher (ed.) et al., Fractional order control and synchronization of chaotic systems. Cham: Springer. Stud. Comput. Intell. 688, 699-718 (2017).
Summary: In this chapter, a new Jerk chaotic system with a piecewise nonlinear (PWNL) function and its fractional-order (FO) generalization are proposed. Both the FO and the PWNL function, serving as chaotic generators, make the proposed system more adopting for electrical engineering applications. The highly complex dynamics of the novel system are investigated by theoretical analysis pointing out its elementary characteristics such as the Lyapunov exponents, the attractor forms and the equilibrium points. To focus on the application values of the novel FO system in multilateral communication, hybrid synchronization (HS) with ring connection is investigated. For such schema, where all systems are coupled on a chain, complete synchronization (CS) and complete anti-synchronization (AS) co-exist where the state variables of the first system couple the \(N\)th system and the state variables of the \(N\)th system couple the \((N-1)\)th system. Simulations results prove that the synchronization problem is achieved with success for the multiple coupled FO systems.
For the entire collection see [Zbl 1410.93005].

MSC:

34A34 Nonlinear ordinary differential equations and systems
34A08 Fractional ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
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