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Anti-Phase Synchronization of the Yu-Wang and Burke-Shaw Chaotic Dynamic Systems via Nonlinear Controllers

Edwin A. Umoh
Department of Electrical Engineering Technology, Federal Polytechnic, Kaura Namoda, Nigeria
Abstract—In this paper, anti-phase synchronization of two non-identical autonomous chaotic systems is presented. These two systems are neither diffeomorphic nor topologically equivalent, but possessed chaotic properties that ease synchronization and antisynchronization based on different control strategies. The Yu-Wang possessed a cross-product quadratic term and a nonlinear hyperbolic term in its algebraic structure while the Burke-Shaw has two nonlinear terms which adds complexity to the system's dynamic evolutions. Nonlinear active controllers were designed to regulate the two exponentially divergent chaotic trajectories of the coupled system to achieve anti-phase synchronization in finite times, while Lyapunov stability theory was employed to test for local and global convergence of the error dynamics to the origin. The results of the various numerical simulations via MATLAB software demonstrates the effectiveness of the coupling scheme and the applicability of the antisynchronized signals in modelling and design of electrical and communications systems that are critical to secure communication and electrical power outage minimization.
 
Index Terms—yu-wang chaotic system, burke-shaw chaotic system, antisynchronization, synchronization, active controllers

Cite: Edwin A. Umoh, "Anti-Phase Synchronization of the Yu-Wang and Burke-Shaw Chaotic Dynamic Systems via Nonlinear Controllers," International Journal of Electronics and Electrical Engineering, Vol. 3, No. 6, pp. 438-444, December 2015. doi: 10.12720/ijeee.3.6.438-444
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