Bifurcation of Discontinuous Limit Cycles of the Van Der Pol Equation
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Date
2014
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Open Access Color
Green Open Access
Yes
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No
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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.
Description
Akhmet, Marat/0000-0002-2985-286X; Turan, Mehmet/0000-0002-1718-3902
Keywords
Discontinuous limit cycle, Van der Pol equation, Hopf bifurcation, Coupled oscillators, Center manifold, discontinuous limit cycle, Bifurcation theory for ordinary differential equations, Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics), Van der Pol equation, Bifurcations of limit cycles and periodic orbits in dynamical systems, Hopf bifurcation, Periodic solutions to ordinary differential equations, Ordinary differential equations with impulses, coupled oscillators, center manifold
Fields of Science
0103 physical sciences, 01 natural sciences
Citation
WoS Q
Q1
Scopus Q
OpenCitations Citation Count
8
Source
Mathematics and Computers in Simulation
Volume
95
Issue
Start Page
39
End Page
54
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Citations
CrossRef : 8
Scopus : 10
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Mendeley Readers : 3
SCOPUS™ Citations
12
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Web of Science™ Citations
9
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Page Views
7
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