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Journal of Vibration Testing and System Dynamics 9(2) (2025) 123--133 | DOI:10.5890/JVTSD.2025.06.003

Mikhail E. Semenov, Olga O. Reshetova, Peter A. Meleshenko, Sergei V. Borzunov, Olesya I. Kanishcheva

Voronezh State University, Univesitetskaya sq.1, Voronezh, Russia

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Abstract

In this article we consider the van der Pol oscillator under hysteresis. In this case there are some peculiarities of the dynamics. We propose a mathematical model that describes the dynamics of a modified van der Pol oscillator with a hysteresis block. In the modified model the quadratic term is replaced by a hysteresis block formalized within the Preisach model. A comparative analysis of the numerical results for the constructed model and the classical van der Pol oscillator is carried out. It is established that chaotic behavior can occur in the modified model unlike the classical case. We also consider a similar model under external excitation. Using the small parameter method, a solution is found, and a comparison of the obtained analytic and numerical results is made. A comparative analysis with the classical forced van der Pol oscillator model is also carried out.

Acknowledgments

This research was supported by the Russian Science Foundation (RSF) grant No. 23-29-00696.

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