Open AccessThe van der Pol oscillator under hysteretic control: regular and chaotic dynamics
Author(s) -
Михаил Е. Семенов,
Olga O. Reshetova,
Vladimir Sobolev,
Andrey M. Solovyov,
Peter A. Meleshenko,
A. N. Bogaychuk
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1368/4/042030
Subject(s) - van der pol oscillator , control theory (sociology) , chaotic , lyapunov exponent , bifurcation , synchronization (alternating current) , physics , coupling (piping) , hysteresis , lyapunov function , work (physics) , nonlinear system , statistical physics , mathematics , control (management) , computer science , engineering , topology (electrical circuits) , quantum mechanics , mechanical engineering , artificial intelligence , combinatorics
In this work we provide the novel hysteretic approach to control the chaotic dynamics of the van der Pol oscillator under periodic excitation. Using the phenomenological Bouc-Wen model, as well as in the frame of the small parameter approach we investigate the influence of the hysteretic control to the dynamical characteristics of this system. Based on the analysis of numerical results in the form of bifurcation diagrams and Lyapunov exponents, the efficiency of the stabilizing role of the hysteretic control element is established. In addition, we investigate the synchronization of oscillations in the system of coupled van der Pol oscillators (with “simple” linear coupling, as well as under hysteretic control). The stabilizing role of the hysteretic control in this case is also demonstrated.