On the Invariant Manifolds of the Fixed Point of a Second-Order Nonlinear Difference Equation

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2020

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Springer/plenum Publishers

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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

This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equationx(n+ 1)=alpha+beta x(n- 1)+x(n- 1)/x(n), where alpha> 0,0 <=beta<1$0\leqslant \beta and the initial conditionsx(- 1)andx(0)are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples.

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Turan, Mehmet/0000-0002-1718-3902
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Turan, Mehmet ORCID logo

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Stable manifold, Unstable manifold, Center manifold, Normal form

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Q3

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Q3

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Volume

26

Issue

4

Start Page

673

End Page

684

URI

https://doi.org/10.1007/s10883-019-09472-3
 https://hdl.handle.net/20.500.14411/3250

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