New fractional chaotic system circuit design and synchronization control

Abstract

Abstract: For a new three-dimensional fractional chaotic system with only one nonlinear term, chaotic characteristics of the system are verified firstly by analyzing phase trajectory, Lyapunov exponent spectrum, power spectrum and Poincare section. Secondly, the stability of the equilibrium point of the system and the bifurcation diagram of the system with respect to fractional order and parameters are studied. The bifurcation diagram shows that the system has abundant chaotic characteristics. Then, a fractional-order chaotic circuit of the system is designed and simulated in software Multisim. The simulation results verify the possibility of realizing the new fractional chaotic system. Finally, the synchronization problem of fractional order systems with disturbances and uncertain parameters is studied. A sliding mode controller based on adaptive control is then designed, and the adaptive laws of unknown disturbances and uncertain parameters are explained reasonably. The synchronization of the system can be realized in the case of both unknown upper bound of the disturbances and parameter uncertainty.

Key words: fractional order, chaotic circuit, adaptive sliding mode control, a non-linear term

CLC Number:

TP273

YAN Min-xiu, XU Hui. New fractional chaotic system circuit design and synchronization control[J]. Journal of Lanzhou University of Technology, 2021, 47(1): 105-112.

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