Dynamics of a Class of Extended Duffing–Van Der Pol Oscillators: Melnikov’s Approach, Simulations, Control over Oscillations

The Duffing–van der Pol oscillator is a very prominent and interesting standard model. There is a substantial body of varied literature on this topic. In this article, we propose a new class of oscillators by adding new factors to its dynamics. Investigations in light of Melnikov’s approach are cons...

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Bibliographic Details
Main Authors: Nikolay Kyurkchiev, Tsvetelin Zaevski, Maria Vasileva, Vesselin Kyurkchiev, Anton Iliev, Asen Rahnev
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/14/2240
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Summary:The Duffing–van der Pol oscillator is a very prominent and interesting standard model. There is a substantial body of varied literature on this topic. In this article, we propose a new class of oscillators by adding new factors to its dynamics. Investigations in light of Melnikov’s approach are considered. Several simulations are composed. A few specialized modules for testing the dynamics of the hypothetical oscillator under consideration are also given. This will be an essential component of a much broader Web-based scientific computing application that is planned. Possible control over oscillations: approximation with restrictions is also discussed; some probabilistic constructions are also presented.
ISSN:2227-7390