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

Peter Dormayer; Anatoli F. Ivanov

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

Peter Dormayer
, Anatoli F. Ivanov

Penn State Wilkes-Barre

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 language	English (US)
Pages (from-to)	61-82
Number of pages	22
Journal	Discrete and Continuous Dynamical Systems
Volume	5
Issue number	1
State	Published - Jan 1 1999

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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

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.",

author = "Peter Dormayer and Ivanov, \{Anatoli F.\}",

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publisher = "American Institute of Mathematical Sciences",

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T1 - Stability of symmetric periodic solutions with small amplitude of ẋ(t) = αf(x(t),x(t - 1))

AU - Dormayer, Peter

AU - Ivanov, Anatoli F.

PY - 1999/1/1

Y1 - 1999/1/1

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.

UR - https://www.scopus.com/pages/publications/0010813253

UR - https://www.scopus.com/pages/publications/0010813253#tab=citedBy

M3 - Article

AN - SCOPUS:0010813253

SN - 1078-0947

VL - 5

SP - 61

EP - 82

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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