Periodic solutions in periodic state-dependent delay equations and population models

Yongkun Li, Yang Kuang

Research output: Contribution to journalArticle

44 Scopus citations

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 languageEnglish (US)
Pages (from-to)1345-1353
Number of pages9
JournalProceedings of the American Mathematical Society
Volume130
Issue number5
DOIs
StatePublished - Jan 1 2002
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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