Extreme multistability in memristive hyper-jerk system and stability mechanism analysis using dimensionality reduction model
Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing 210094, P.R. China
2 School of Information Science and Engineering, Changzhou University, Changzhou 213164, P.R. China
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Received in final form: 10 April 2019
Published online: 14 October 2019
This paper presents a memristive hyper-jerk system with smooth hyperbolic tangent memductance nonlinearity. Such a smooth memductance nonlinearity can cause the system to possess a line equilibrium therein, leading to the emergence of extreme multistability with coexisting infinitely many attractors due to the existence of a zero eigenvalue. To illustrate the stability mechanism, the dimensionality reduction model of the memristive hyper-jerk system is obtained using state variable mapping (SVM) method and several isolated equilibria are yielded from the dimensionality reduction model. As a consequence, the initial-dependent extreme multistability in the memristive hyper-jerk system is converted into the initial-related parameter-dependent dynamics in the dimensionality reduction model and the stability mechanism analysis is thereby executed. Furthermore, PSIM circuit simulations based on a physical circuit are performed to confirm the coexisting infinitely many attractors.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019