Bifurcation of discontinuous limit cycles of the Van der Pol equation

Date

2014-01-01

Author

Akhmet, Marat

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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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URI

https://hdl.handle.net/11511/32762

Journal

MATHEMATICS AND COMPUTERS IN SIMULATION

DOI

https://doi.org/10.1016/j.matcom.2013.05.002

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Department of Mathematics, Article

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Citation Formats

M. Akhmet, “Bifurcation of discontinuous limit cycles of the Van der Pol equation,” MATHEMATICS AND COMPUTERS IN SIMULATION, pp. 39–54, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32762.