Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

ABSTRACT

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master–slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

KEYWORDS:

• Chaotic flows
• anti-monotonicity
• circuit design
• synchronisation
• dynamic sliding surface

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Saleh Mobayen

Saleh Mobayen was born in Khoy, Iran, in December 1983. He received the B.S. and M.Sc. degrees in Control Engineering from the University of Tabriz, Tabriz, Iran, in 2007 and 2009, respectively, and received his Ph.D. in Control Engineering from Tarbiat Modares University, Tehran, Iran, in 2012. Since 2013, he has been as an Assistant Professor and faculty member with the Department of Electrical Engineering of University of Zanjan, Zanjan, Iran. He has published several papers in the national and international Journals. He is a member of IEEE and serves as a member of program committee of several international conferences. His research interests include control theory, sliding mode control, robust tracking, non-holonomic robots and chaotic systems.

Sifeu Takougang Kingni

Sifeu Takougang Kingni was born in Douala, Cameroon, in 1984. He received a M.Sc. degree in Mechanics in 2008 from the University of Yaoundé I, Cameroon and in 2014 a joint Ph.D. degree in Mechanics between the Vrije Universiteit Brussel, Brussels, Belgium and the University of Yaoundé I, Cameroon. He is as a Lecturer at the Department of Mechanical and Electrical Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, Cameroon. He has published several papers in international Journals and serves as a reviewer of several international Journals. His research interests include nonlinear dynamics of semiconductor lasers, electronic circuits, optomechanics, synchronization of chaotic systems and secure communications.

Viet-Thanh Pham

Viet-Thanh Pham received the degree in electronics and telecommunications from the Hanoi University of Technology, Vietnam, in 2005, and the Ph.D. degree in electronics, automation and control of complex systems engineering from the University of Catania, Italy, in 2013. He has been a Lecturer with the School of Electronics and Telecommunications, Hanoi University of Science and Technology, since 2013. His scientific interest includes chaos, nonlinear control, applications of nonlinear systems, analysis and design of analog circuits, and FPGA-based digital circuits.

Fahimeh Nazarimehr

Fahimeh Nazarimehr was born in 1990 in Qazvin, Iran. She receives the B.Sc. degree in biomedical engineering at Shahed University in 2012 and the M.Sc. degree at Sharif University of Technology in 2014. She is currently a PhD student in biomedical engineering at Amirkabir University of Technology. Her research interests include chaos theory and its application in biological signals and systems, nonlinear dynamics, bifurcation analysis, dynamical systems in neuroscience, bio-electricity and quantitative approaches, and feature extraction and classification of signals.

Sajad Jafari

Sajad Jafari was born in Kermanshah, Iran, in 1983. He received his BSc., M.S., and Ph.D. degrees in biomedical engineering in 2005, 2008, 2013 from biomedical engineering department, Amirkabir University of technology, Tehran, Iran. He is currently an assistant professor in there (since 2013). His research interests include artificial intelligence, optimization, pattern recognition and especially nonlinear and chaotic signals and systems. He has published more than 100 SCI (ISI) indexed papers.