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

Authors: Yongkun Li and Yang Kuang
Journal: Proc. Amer. Math. Soc. 130 (2002), 1345-1353
MSC (2000): Primary 34K13; Secondary 34K20, 92D25
Published electronically: December 27, 2001
MathSciNet review: 1879956
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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.

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Additional Information

Yongkun Li
Affiliation: Department of Mathematics, Yunnan University, Kunming, People’s Republic of China

Yang Kuang
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287

Keywords: Coincidence degree, periodic solution, delay equation, state-dependent delay, population model
Received by editor(s): July 1, 2000
Published electronically: December 27, 2001
Additional Notes: The second author’s research was partially supported by NSF Grant DMS-0077790
Communicated by: Suncica Canic
Article copyright: © Copyright 2001 American Mathematical Society