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Advances in Memristors, Memristive Devices and Systems pp 393–423Cite as

A Conservative Hyperchaotic Hyperjerk System Based on Memristive Device

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 701))

Abstract

Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention in the control literature. In this work, we propose a conservative memristor-based hyperchaotic hyperjerk system with infinite number of equilibrium points. In classical mechanics, the third-order time-derivative of displacement is called jerk, while the fourth-order time-derivative of displacement is called snap. As a result, a dynamical system which is represented by an nth order ordinary differential equation with \(n > 3\) is considered as a hyperjerk system. Hyperjerk systems have received significant attention in the control literature. In this research work, a conservative memristor-based hyperjerk system has been designed which displays rich, hyperchaotic behavior. Interestingly, this hyperjerk system displays an infinite number of equilibrium points because of the presence of a memristive device. In this work, we obtain the Lyapunov exponents of the memristor-based system as \(L_1 = 0.2098\), \(L_2 = 0.2035\), \(L_3 = 0\) and \(L_4 = -0.4133\). Since there are two positive Lyapunov exponents, the memristor-based system is hyperchaotic. Also, the Kaplan-Yorke dimension of the memristor-based hyperchaotic system is obtained as \(D_{KY} = 4\). Next, we design adaptive control and synchronization schemes for the memristor-based hyperjerk system with unknown parameters via backstepping control method. The main adaptive control and synchronization results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the main results of this work.

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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. Sundarapandian Vaidyanathan
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  1. Research and Development Centre, Vel Tech University Research and Development Centre, Chennai, India

    Sundarapandian Vaidyanathan

  2. Department of Physics, Aristotle University of Thessaloniki Department of Physics, Thessaloniki, Greece

    Christos Volos

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Vaidyanathan, S. (2017). A Conservative Hyperchaotic Hyperjerk System Based on Memristive Device. In: Vaidyanathan, S., Volos, C. (eds) Advances in Memristors, Memristive Devices and Systems. Studies in Computational Intelligence, vol 701. Springer, Cham. https://doi.org/10.1007/978-3-319-51724-7_16

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