Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = extended oscillator based on Duffing–van der Pol oscillator

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
21 pages, 1261 KB  
Article
Dynamics of a Class of Extended Duffing–Van Der Pol Oscillators: Melnikov’s Approach, Simulations, Control over Oscillations
by Nikolay Kyurkchiev, Tsvetelin Zaevski, Maria Vasileva, Vesselin Kyurkchiev, Anton Iliev and Asen Rahnev
Mathematics 2025, 13(14), 2240; https://doi.org/10.3390/math13142240 - 10 Jul 2025
Cited by 2 | Viewed by 1992
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Chaos Theory and Complexity)
Show Figures

Figure 1

21 pages, 1809 KB  
Article
Dynamics of a Class of Chemical Oscillators with Asymmetry Potential: Simulations and Control over Oscillations
by Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev and Asen Rahnev
Mathematics 2025, 13(7), 1129; https://doi.org/10.3390/math13071129 - 29 Mar 2025
Cited by 3 | Viewed by 1125
Abstract
The literature devoted to the issue of a forced modified Van der Pol–Duffing oscillator with asymmetric potential is a major and varied way to represent nonlinear dissipative chemical dynamics. It is known that this model is based on the real reaction–kinetic scheme. In [...] Read more.
The literature devoted to the issue of a forced modified Van der Pol–Duffing oscillator with asymmetric potential is a major and varied way to represent nonlinear dissipative chemical dynamics. It is known that this model is based on the real reaction–kinetic scheme. In this paper, we suggest a novel class of oscillators that are appealing to users due to their numerous free parameters and asymmetric potential. The rationale for this is because an expanded model is put out that enables the investigation of both classical and more recent models that have been reported in the literature at a “higher energy level”. We present a few specific modules for examining these oscillators’ behavior. A much broader Web-based application for scientific computing will incorporate this as a key component. Probabilistic construction to offer possible control over the oscillations is also considered. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation)
Show Figures

Figure 1

Back to TopTop