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A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Hyperchaos, Control, Synchronization and Circuit Simulation of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities

Authors : Sundarapandian Vaidyanathan, Christos K. Volos, Viet-Thanh Pham

Published in: Advances in Chaos Theory and Intelligent Control

Publisher: Springer International Publishing

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Abstract

In this work, we announce an eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities. The novel 4-D hyperchaotic system has been derived by adding a feedback control to the seven term 3-D Lu-Xiao chaotic system [1]. The phase portraits of the eleven-term novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel hyperchaotic system has a unique equilibrium at the origin, which is a saddle point. Thus, the origin is an unstable equilibrium of the novel hyperchaotic system. The Lyapunov exponents of the novel hyperchaotic system are obtained as \(L_1 = 1.6023, L_2 = 0.1123, L_3 = 0\) and \(L_4 = -22.6467\). Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is obtained as \(D_{KY} = 3.0757\). Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical hyperchaotic systems with unknown parameters. Finally, an electronic circuit realization of the novel 4-D hyperchaotic system using SPICE is described in detail to confirm the feasibility of the theoretical model.

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previous chapter Generalized Projective Synchronization of a Novel Hyperchaotic Four-Wing System via Adaptive Control Method
next chapter Complete Synchronization of Hyperchaotic Systems via Novel Sliding Mode Control
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Metadata
Title
Hyperchaos, Control, Synchronization and Circuit Simulation of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities
Authors
Sundarapandian Vaidyanathan
Christos K. Volos
Viet-Thanh Pham
Copyright Year
2016
Book
Advances in Chaos Theory and Intelligent Control

Print ISBN: 978-3-319-30338-3

Electronic ISBN: 978-3-319-30340-6

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-30340-6_13

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