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A Novel 2-D Chaotic Enzymes-Substrates Reaction System and Its Adaptive Backstepping Control

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Advances in Chaos Theory and Intelligent Control

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 337))

Abstract

In this research work, we announce a novel 2-D chaotic enzymes-substrates reaction system and discuss its adaptive backstepping control. First, this work describes the dynamic equations and qualitative properties of the novel 2-D biological chaotic system. Our novel chaotic system is obtained by modifying the equations of the 2-D enzymes-substrates reaction system with ferroelectric behaviour in brain waves obtained by Kadji et al. (Chaos Solitons Fractals 32:862–882, 2001, [27]). The Maximal Lyapunov Exponent (MLE) of the novel 2-D chaotic enzymes-substrates reaction system is obtained as \(L_1 = 0.14425\). Next, this work describes the adaptive control of the novel 2-D chaotic enzymes-substrates reaction system via backstepping control method. Furthermore, this work describes the adaptive synchronization of identical novel 2-D chaotic enzymes-substrates reaction systems via backstepping control method. The main stabilization and synchronization results derived in this work are established via Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this work for the novel 2-D chaotic enzymes-substrates reaction system.

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  1. Research and Development Centre, Vel Tech University, Avadi, Chennai, 600062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

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  1. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

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Vaidyanathan, S. (2016). A Novel 2-D Chaotic Enzymes-Substrates Reaction System and Its Adaptive Backstepping Control. In: Azar, A., Vaidyanathan, S. (eds) Advances in Chaos Theory and Intelligent Control. Studies in Fuzziness and Soft Computing, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-319-30340-6_21

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