Title: A new three-dimensional chaotic system: its adaptive control and circuit design

Authors: Sundarapandian Vaidyanathan; Oumate Alhadji Abba; Gambo Betchewe; Mohamadou Alidou

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai 600062, Tamil Nadu, India ' Department of Physics, The Faculty of Science, The University of Maroua, Cameroon ' Department of Physics, The Faculty of Science, The University of Maroua, Cameroon ' Department of Physics, The Faculty of Science, The University of Maroua, Cameroon; The Abdus Salam International Centre for Theoretical Physics, Strada costiera 11, 1-34014, Trieste, Italy

Abstract: A new three-dimensional chaotic system with two nonlinearities is proposed in this research work. Specifically, the two nonlinearities considered in the construction of the new chaotic system are a quadratic nonlinearity and a quartic nonlinearity. A systematic study of the three-dimensional chaotic system has been made including phase portraits, dissipativity, rest points and their stability, Lyapunov chaos exponents, Kaplan-Yorke fractal dimension, etc. As main control results, we design feedback control laws using adaptive control theory to achieve global stabilisation of the new chaotic system and also global synchronisation of identical chaotic systems with unknown parameters. Finally, an electronic circuit design of the new chaotic system using electronic work bench (EWB) is described in detail to confirm the feasibility of the theoretical chaotic model.

Keywords: chaos; chaos control; chaos synchronisation; adaptive control; circuit design.

DOI: 10.1504/IJAAC.2019.096420

International Journal of Automation and Control, 2019 Vol.13 No.1, pp.101 - 121

Received: 06 Nov 2017
Accepted: 24 Nov 2017
Published online: 28 Nov 2018 *

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