### 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 1999 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems*,

*5*(1), 61-82.

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*Discrete and Continuous Dynamical Systems*, vol. 5, no. 1, pp. 61-82.

**Stability of symmetric periodic solutions with small amplitude of ẋ(t) = αf(x(t),x(t - 1)).** / Dormayer, Peter; Ivanov, Anatoli.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Dormayer, Peter

AU - Ivanov, Anatoli

PY - 1999/1

Y1 - 1999/1

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 - http://www.scopus.com/inward/record.url?scp=0010813253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010813253&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 61

EP - 82

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 1

ER -