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A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

Sundarapandian Vaidyanathan, Ahmad Taher Azar, Aceng Sambas, Shikha Singh, Kammogne Soup Tewa Alain, Fernando E. Serrano
Copyright: © 2018 |Pages: 38
ISBN13: 9781522540779|ISBN10: 1522540776|EISBN13: 9781522540786
DOI: 10.4018/978-1-5225-4077-9.ch013
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MLA

Vaidyanathan, Sundarapandian, et al. "A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation." Advances in System Dynamics and Control, edited by Ahmad Taher Azar and Sundarapandian Vaidyanathan, IGI Global, 2018, pp. 382-419. https://doi.org/10.4018/978-1-5225-4077-9.ch013

APA

Vaidyanathan, S., Azar, A. T., Sambas, A., Singh, S., Alain, K. S., & Serrano, F. E. (2018). A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation. In A. Azar & S. Vaidyanathan (Eds.), Advances in System Dynamics and Control (pp. 382-419). IGI Global. https://doi.org/10.4018/978-1-5225-4077-9.ch013

Chicago

Vaidyanathan, Sundarapandian, et al. "A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation." In Advances in System Dynamics and Control, edited by Ahmad Taher Azar and Sundarapandian Vaidyanathan, 382-419. Hershey, PA: IGI Global, 2018. https://doi.org/10.4018/978-1-5225-4077-9.ch013

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Abstract

This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

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