Title: Extreme multi-stability in hyperjerk memristive system with hidden attractors and its adaptive synchronisation scheme

Authors: Dimitrios A. Prousalis; Christos K. Volos; Ioannis N. Stouboulos; Ioannis M. Kyprianidis

Addresses: Laboratory of Nonlinear Systems - Circuits and Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR - 54124, Greece ' Laboratory of Nonlinear Systems - Circuits and Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR - 54124, Greece ' Laboratory of Nonlinear Systems - Circuits and Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR - 54124, Greece ' Laboratory of Nonlinear Systems - Circuits and Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR - 54124, Greece

Abstract: This paper presents a study of the phenomenon of extreme multi-stability in a novel 4D hyperjerk memristive system. The proposed system appertains to the category of dynamical systems with hidden attractors due to infinite equilibrium points. The behaviour of the system is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram and Lyapunov exponents. Also, this work showed that the extreme multi-stability phenomenon of the behaviour of infinitely many coexisting attractors depends on the initial conditions of the variables of the system. Moreover, the case of chaos synchronisation of the system with unknown parameters, using adaptive synchronisation method, is investigated.

Keywords: memristor; memristive systems; hyperjerk systems; extreme multi-stability; hidden attractors; adaptive control.

DOI: 10.1504/IJSPM.2018.094737

International Journal of Simulation and Process Modelling, 2018 Vol.13 No.5, pp.433 - 445

Received: 28 Dec 2017
Accepted: 27 Mar 2018
Published online: 14 Sep 2018 *

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