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A Seven-Term Novel Jerk Chaotic System and Its Adaptive Control

  • Sundarapandian Vaidyanathan
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 636)

Abstract

In this work, we describe a seven-term novel 3-D jerk chaotic system with two nonlinearities (quadratic and cubic). The phase portraits of the novel jerk chaotic system are displayed and the dynamic properties of the novel jerk chaotic system are discussed. The novel jerk chaotic system has three saddle-foci equilibrium points, which are unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as \(L_1 = 0.5565, L_2 = 0\) and \(L_3 = -1.5566\). The Kaplan–Yorke dimension of the novel jerk chaotic system is obtained as \(D_{KY} = 2.3575\). Next, an adaptive backstepping controller is designed to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been shown to illustrate all the main results derived in this work.

Keywords

Chaos Chaotic systems Jerk systems Backstepping control Adaptive control Synchronization 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Research and Development CentreVel Tech UniversityAvadi, ChennaiIndia

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