### 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) |
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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

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## Cite this

Dormayer, P., & Ivanov, A. F. (1999). Stability of symmetric periodic solutions with small amplitude of ẋ(t) = αf(x(t),x(t - 1)).

*Discrete and Continuous Dynamical Systems*,*5*(1), 61-82.