Eur. Phys. J. Special Topics 228, 1995-2009 (2019)
https://doi.org/10.1140/epjst/e2019-800238-0

Regular Article

Extreme multistability in memristive hyper-jerk system and stability mechanism analysis using dimensionality reduction model

¹ 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

^a e-mail: mervinbao@126.com

Received: 27 December 2018
Received in final form: 10 April 2019
Published online: 14 October 2019

Abstract

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.