Solution behaviour in a class of difference-differential equations

A. D. Fedorenko, V. V. Fedorenko, Anatoli Ivanov, A. N. Sharkovsky

Research output: Contribution to journalReview article

6 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)37-47
Number of pages11
JournalBulletin of the Australian Mathematical Society
Volume57
Issue number1
StatePublished - Feb 1998

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Difference-differential Equations
Delay Differential Equations
Difference equation
Bifurcation
Finite Difference Equation
Neutral Type
Piecewise continuous
Continuous Dependence
Singular Perturbation
Singularly Perturbed
Small Parameter
Nonlinearity
First-order
Interval
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Fedorenko, A. D. ; Fedorenko, V. V. ; Ivanov, Anatoli ; Sharkovsky, A. N. / Solution behaviour in a class of difference-differential equations. In: Bulletin of the Australian Mathematical Society. 1998 ; Vol. 57, No. 1. pp. 37-47.
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Fedorenko, AD, Fedorenko, VV, Ivanov, A & Sharkovsky, AN 1998, 'Solution behaviour in a class of difference-differential equations', Bulletin of the Australian Mathematical Society, vol. 57, no. 1, pp. 37-47.

Solution behaviour in a class of difference-differential equations. / Fedorenko, A. D.; Fedorenko, V. V.; Ivanov, Anatoli; Sharkovsky, A. N.

In: Bulletin of the Australian Mathematical Society, Vol. 57, No. 1, 02.1998, p. 37-47.

Research output: Contribution to journalReview article

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AU - Fedorenko, V. V.

AU - Ivanov, Anatoli

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N2 - 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.

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