Stability of symmetric periodic solutions with small amplitude of ẋ(t) = αf(x(t),x(t - 1))

Peter Dormayer, Anatoli Ivanov

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We study special symmetric periodic solutions of the equation ẋ(t) = αf(x(t), x(t - 1)) where α is a positive parameter and the nonlinearity f satisfies the symmetry conditions f(-u,v) = -f(u,-v) = f(u,v) . We establish the existence and stability properties for such periodic solutions with small amplitude.

Original languageEnglish (US)
Pages (from-to)61-82
Number of pages22
JournalDiscrete and Continuous Dynamical Systems
Volume5
Issue number1
StatePublished - Jan 1999

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Periodic Solution
Nonlinearity
Symmetry

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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abstract = "We study special symmetric periodic solutions of the equation ẋ(t) = αf(x(t), x(t - 1)) where α is a positive parameter and the nonlinearity f satisfies the symmetry conditions f(-u,v) = -f(u,-v) = f(u,v) . We establish the existence and stability properties for such periodic solutions with small amplitude.",
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Stability of symmetric periodic solutions with small amplitude of ẋ(t) = αf(x(t),x(t - 1)). / Dormayer, Peter; Ivanov, Anatoli.

In: Discrete and Continuous Dynamical Systems, Vol. 5, No. 1, 01.1999, p. 61-82.

Research output: Contribution to journalArticle

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N2 - We study special symmetric periodic solutions of the equation ẋ(t) = αf(x(t), x(t - 1)) where α is a positive parameter and the nonlinearity f satisfies the symmetry conditions f(-u,v) = -f(u,-v) = f(u,v) . We establish the existence and stability properties for such periodic solutions with small amplitude.

AB - We study special symmetric periodic solutions of the equation ẋ(t) = αf(x(t), x(t - 1)) where α is a positive parameter and the nonlinearity f satisfies the symmetry conditions f(-u,v) = -f(u,-v) = f(u,v) . We establish the existence and stability properties for such periodic solutions with small amplitude.

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