Details

Title

Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

Journal title

Archives of Control Sciences

Yearbook

2016

Numer

No 4

Publication authors

Divisions of PAS

Nauki Techniczne

Abstract

<jats:title>Abstract</jats:title> <jats:p> This research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L<jats:sub>1</jats:sub> = 3.1575, L<jats:sub>2</jats:sub> = 0.3035, L<jats:sub>3</jats:sub> = 0 and L<jats:sub>4</jats:sub> = −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as D<jats:sub>KY</jats:sub> = 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work.</jats:p>

Publisher

Committee of Automatic Control and Robotics PAS

Date

2016

Identifier

ISSN 1230-2384

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DOI

10.1515/acsc-2016-0026

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