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Archives of Control Sciences

The Journal of Polish Academy of Sciences

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Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

Sundarapandian Vaidyanathan
  • Corresponding author
  • Research and Development Centre, Vel Tech University, Avadi, Chennai- 600062, Tamilnadu, India
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Christos Volos / Viet-Thanh Pham
  • School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-12-17 | DOI: https://doi.org/10.2478/acsc-2014-0023

Abstract

In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684,L2 = 0.2174,L3 = 0 and L4 =−12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as DKY =3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195,L2 = 0.2430,L3 = 0.0145,L4 = 0 and L5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as DKY =4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.

Keywords: chaos; hyperchaos; control; synchronization; circuit realization

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About the article

Received: 2014-09-29

Published Online: 2014-12-17

Published in Print: 2014-12-01


Citation Information: Archives of Control Sciences, Volume 24, Issue 4, Pages 409–446, ISSN (Online) 2300-2611, DOI: https://doi.org/10.2478/acsc-2014-0023.

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© Archives of Control Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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