Title: Oscillations and hysteresis: from simple harmonic oscillator and unusual unbounded increasing amplitude phenomena to the van der Pol oscillator and chaos control

Authors: Mikhail E. Semenov; Olga O. Reshetova; Peter A. Meleshenko; Alexander F. Klinskikh

Addresses: Digital Technologies Department, Voronezh State University, Russia; Mathematics Department, Voronezh State Technical University, Russia; Geophysical Survey of Russia Academy of Sciences, Obninsk, Russia; Meteorology Department, Zhukovsky-Gagarin Air Force Academy, Voronezh, Russia ' Digital Technologies Department, Voronezh State University, Voronezh, Russia ' Digital Technologies Department, Voronezh State University, Voronezh, Russia; Target Search Lab of Groundbreaking Radio Communication Technologies of Advanced Research Foundation, Voronezh, Russia ' General Physics Department, Voronezh State University, Voronezh, Russia

Abstract: In this work we investigate various oscillating systems under hysteretic action. For a simple harmonic oscillator under hysteretic force an unusual unbounded increasing amplitude phenomena (growing rate for the amplitude is proportional to square root of time) are obtained and discussed. For a system of coupled van der Pol oscillators (taking into account the hysteretic coupling) we investigate various dynamic regimes (both regular and chaotic) and show that the hysteresis in the link between two van der Pol oscillators may serve as an effective mechanism for chaos control. Also we consider the effect of hysteresis on synchronisation processes in this system.

Keywords: hysteresis; Bouc-Wen model; van der Pol oscillator; regular and chaotic dynamics; synchronisation.

DOI: 10.1504/IJESMS.2020.111274

International Journal of Engineering Systems Modelling and Simulation, 2020 Vol.11 No.4, pp.147 - 159

Received: 25 Sep 2019
Accepted: 23 Mar 2020
Published online: 17 Nov 2020 *

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