Bifurcation of discontinuous limit cycles of the Van der Pol equation

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2014

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Elsevier

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

In this paper, we apply the methods of B-equivalence and psi-substitution to prove the existence of discontinuous limit cycle for the Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. The main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to demonstrate the theoretical results as well as application opportunities. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

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Akhmet, Marat/0000-0002-2985-286X; Turan, Mehmet/0000-0002-1718-3902
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Akhmet, Marat ORCID logo
Turan, Mehmet ORCID logo

Keywords

Discontinuous limit cycle, Van der Pol equation, Hopf bifurcation, Coupled oscillators, Center manifold

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8

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Volume

95

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Start Page

39

End Page

54

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https://doi.org/10.1016/j.matcom.2013.05.002
 https://hdl.handle.net/20.500.14411/136

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