Extreme multistability in memristor-based hypogenetic jerk system

Significance 

Chaos is an interesting nonlinear phenomenon that focuses on the behavior of dynamical systems that are highly sensitive to initial conditions. Additionally, it can be obtained from a class of nonlinear dynamical systems described by a set of autonomous ordinary differential equations. Basically, intricate nonlinear phenomena in various nonlinear dynamical systems can be experimentally measured and successfully validated from the implementation circuits. Memristor-based nonlinear dynamical system easily presents the initial condition dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors, which has been receiving much research attention in recent years. Recently published papers have highlighted the emergence of extreme multistability which has been seen to affect the engineering applicability of the nonlinear dynamical system, and has also generated challenges for the switching controls of the multiple stable states. Therefore, it is imperative that an investigation of the coexisting multiple or infinitely many attractors and the corresponding physical hardware implementation be undertaken as it would play a vital role in theoretical studies and information engineering applications.

Changzhou University scientists: Han Bao (PhD candidate), Ning Wang (PhD candidate), Professor Bocheng Bao, Associate professor Mo Chen at in collaboration with Ms Peipei Jin, Professor Guangyi Wang at Hangzhou Dianzi University introduced an ideal and active flux-controlled memristor with absolute value nonlinearity into an existing hypogenetic chaotic jerk system. Their work is currently published in the research journal, Communications in Nonlinear Science and Numerical Simulation.

Briefly, the research method employed commenced with the introduction of the novel memristor-based hypogenetic jerk system with four-line equilibria, after which the stability of the four-line equilibria were explored. Next, the researchers investigated the initial conditions dependent extreme multistability by bifurcation diagrams and Lyapunov exponent spectra. Lastly, they designed an implementation circuit and performed PSIM (Power Simulation) circuit simulations in order to verify the initial conditions-dependent dynamical behaviors of coexisting infinitely many attractors and transient period in the memristive hypogenetic jerk system.

The authors observed that the coexisting infinitely many attractors’ behavior was revealed by attraction basins and phase portraits. The research team also noted that the unusual transition behavior of long-term transient period with steady chaos, entirely different from the phenomenon of transient chaos, was found for some initial conditions. Moreover, from the hardware circuit designed and fabricated, the truth of extreme multistability was verified.

In a nutshell, the study presented an interesting memristor-based chaotic system with hypogenetic jerk equation and circuit forms, which was constructed by introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system. Generally, they observed that the system had four-line equilibria and exhibited an initial condition-dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors. Altogether, it can be concluded that the limit cycles and chaotic attractors exhibited in the memristor based hypogenetic jerk system are all self-existed attractors, rather than hidden attractors.

Extreme multistability in memristor-based hypogenetic jerk system - Advances Engineering

About the author

Han Bao received the B.S. degree from Finance and Economics University of Jiangxi, China, in 2015 and the M.S. degree from Changzhou University, China, in 2018. He is currently pursuing the Ph.D. degree in nonlinear system analysis and measurement technology at Nanjing University of Aeronautics and Astronautics, China. His research interest includes memristive neuromorphic circuit, computer science, and artificial intelligence.

About the author

Bocheng Bao received the B.S. and M.S. degrees in electronic engineering from the University of Electronics Science and Technology of China, Chengdu, China, in 1986 and 1989, respectively, and the Ph.D. degree with the Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing, China, in 2010.

He has more than 20 years’ experience in industry and has ever been on several enterprises serving as Senior Engineer and General Manager. From June 2008 to January 2011, he was a Professor in the School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou, China. He is currently a Professor in the School of Information Science and Engineering, Changzhou University, Changzhou, China. From June 2013 to December 2013, he was with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada, as a Visiting Scholar.

His research interests include bifurcation and chaos, analysis and simulation in neuromorphic circuits, power electronic circuits, and nonlinear circuits and systems.

About the author

Ning Wang received the B.Sc. and M.Sc. degree in electronic information engineering and computer application technology from Changzhou University, Changzhou, China, in 2015 and 2018, respectively. He is currently pursuing the Ph.D. degree in control science and engineering at Tianjin University, Tianjin, China.

His research interest includes the design and application of chaotic circuits and systems, dynamics analysis of nonlinear circuits and systems.

About the author

Mo Chen received the B.S. in information engineering, and the M.S. and Ph.D. degrees in Electromagnetic Field and Microwave Technology from Southeast University, Nanjing, China, in 2003, 2006 and 2009, respectively.

From March 2009 to July 2013, she was a Lecturer in Southeast University, Nanjing, China. Now, she is an associate professor in the School of Information Science and Engineering, Changzhou University, Changzhou, China.

Her research interest mainly focuses on memristor and its application circuits, and other nonlinear circuits and systems.

About the author

Peipei Jin received the B.S. degree in Electronic Information Engineering from Hebei University of Science and Technology, Hebei, China, in 2014, the M.S. degree in Electronic and Communication Engineering from Hangzhou Dianzi University, Hangzhou, China, in 2017. She is currently an assistant at the National Engineering Research Center for Software Engineering, Peking University.

Her research interests include nonlinear circuits and systems, chaotic circuits, locally active memristor.

About the author

Guangyi Wang received the B.S. degree in Physics from Binzhou University, Binzhou, China, in 1980, the M.S. degree in Theoretical Electrical Engineering from Hunan University, Changsha, China, in 1986, and the Ph.D. degree in Electronic Science and Technology from South China University of Technology, Guangzhou, China, in 2004.

From 1996 to 2003, he was a Professor with the Physics Department, Binzhou University. Since 2003, he has been a Professor with the School of Electronic Information, Hangzhou Dianzi University.

He is the author of two books, more than 110 articles, and more than 20 inventions. His research interests include nonlinear circuits and systems, chaotic circuits, signal processing.

Reference

Han Bao, Ning Wang, Bocheng Bao, Mo Chen, Peipei Jin, Guangyi Wang. Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria. Communications in Nonlinear Science and Numerical Simulation Volume 57,  2018, Pages 264-275

Go To Communications in Nonlinear Science and Numerical Simulation

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