Abstract
This paper introduces a fractional order memristor no equilibrium (FOMNE) chaotic system and investigates its adaptive sliding mode synchronization. Firstly the dynamic properties of the integer order memristor no equilibrium system are analyzed. The fractional order memristor no equilibrium system is then derived from the integer order model. Lyapunov exponents and bifurcation with fractional order are investigated. An adaptive sliding mode control algorithm is derived to globally synchronize the identical fractional order memristor systems and genetically optimized fractional order PID controllers are designed and used to synchronize the FOMNE systems. Finally the fractional order memristor no equilibrium system is realized using FPGA.
Highlights
Chaotic systems are a special case of nonlinear systems which can be categorized as chaotic if the system possesses at least one positive Lyapunov exponent and hyperchaotic if the system possesses two or more positive Lyapunov exponents
We introduce a novel 4D memristor no equilibrium chaotic system (MNECS) with three parameters derived from the Sundarapandian system [46] by including a fourth state which is a combination of state feedback and the flux controlled memristor [47, 48] as described by ẋ = az + xy ẏ = 1 − x2 − z2 − w2 (1)
The dynamic properties of the proposed system are investigated to prove the chaotic behavior of the system
Summary
Chaotic systems are a special case of nonlinear systems which can be categorized as chaotic if the system possesses at least one positive Lyapunov exponent and hyperchaotic if the system possesses two or more positive Lyapunov exponents. Chaotic systems with no equilibrium are of great interest in chaos literature. Fractional order controllers [24,25,26,27, 36,37,38] are more effective compared to its integer order models especially in chaos control and synchronization. Fractional order systems with no equilibrium are announced and investigated by Li and Chen [39]. In this paper we announce a novel integer order memristor no equilibrium chaotic system. We derive a fractional order model of the proposed novel system. The dynamic properties of both integer order and fractional order novel systems are investigated. A fractional order adaptive sliding mode control and genetically optimized fractional order PID are proposed to synchronize the identical novel fraction order systems. The proposed fractional order system is implemented in FPGA
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