### Abstract

Sufficient and realistic conditions are obtained for the existence of positive periodic solutions in periodic equations with state-dependent delay. The method involves the application of the coincidence degree theorem and estimations of uniform upper bounds on solutions. Applications of these results to some population models are presented. These application results indicate that seasonal effects on population models often lead to synchronous solutions. In addition, we may conclude that when both seasonality and time delay are present and deserve consideration, the seasonality is often the generating force for the often observed oscillatory behavior in population densities.

Original language | English (US) |
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Pages (from-to) | 1345-1353 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2002 |

Externally published | Yes |

### Keywords

- Coincidence degree
- Delay equation
- Periodic solution
- Population model
- State-dependent delay

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics