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Solution behaviour in a class of difference–differential equations

Published online by Cambridge University Press:  17 April 2009

A.D. Fedorenko ,
V.V. Fedorenko ,
A.F. Ivanov  and
A.N. Sharkovsky
A.D. Fedorenko
Affiliation:
Institute of MathematicsNational Academy of Sciences of UkraineKiveUkraine
V.V. Fedorenko
Affiliation:
Institute of MathematicsNational Academy of Sciences of UkraineKiveUkraine
A.F. Ivanov
Affiliation:
CADSEM and School of Computing and MathematicsDeakin UniversityMelbourne VicAustralia and Institute of MathematicsNational Academy of Sciences of UkraineKiveUkraine
A.N. Sharkovsky
Affiliation:
Institute of MathematicsNational Academy of Sciences of UkraineKiveUkraine
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Abstract

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Difference equations with piecewise continuous nonlinearities and their singular perturbations, first order neutral type delay differential equations with small parameters, are considered. Solutions of the difference equations are shown to be asymptotically periodic with period-adding bifurcations and bifurcations determined by Farey's rule taking place for periods and types of solutions. Solutions of the singularly perturbed delay differential equations are considered and compared with solutions of the difference equations within finite time intervals. The comparison is based on a continuous dependence of solutions on the singular parameter.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 37 - 48
Copyright
Copyright © Australian Mathematical Society 1998

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