Bifurcation of three-dimensional discontinuous cycles

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2009

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Pergamon-elsevier Science Ltd

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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

We consider three-dimensional discontinuous dynamical systems with non-fixed moments of impacts. Existence of the center manifold is proved for the system. The result is applied for the extension of the planar Hopf bifurcation theorem [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163-178]. Illustrative examples are constructed for the theory. (C) 2009 Elsevier Ltd. 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

Impulsive differential equations, Hopf bifurcation, The center manifold

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5

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71

Issue

12

Start Page

E2090

End Page

E2102

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https://doi.org/10.1016/j.na.2009.03.071
 https://hdl.handle.net/20.500.14411/1522

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