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arXiv · 1607.05041

Periodic solutions for a non-monotone family of delayed differential equations with applications to Nicholson systems

Teresa Faria
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Abstract

For a family of $n$-dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics, the existence of a positive periodic solution is obtained under very mild conditions. The proof uses the Schauder fixed point theorem and relies on the permanence of the system. A general criterion for the existence of a positive periodic solution for Nicholson's blowflies periodic systems (with both distributed and discrete time-varying delays) is derived as a simple application of our main result, generalizing the few existing results concerning multi-dimensional Nicholson models. In the case of a Nicholson system with discrete delays all multiples of the period, the global attractivity of the positive periodic solution is further analyzed, improving results in recent literature.

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Teresa Faria. 2016-07-18. Periodic solutions for a non-monotone family of delayed differential equations with applications to Nicholson systems. https://doi.org/10.1016/j.jde.2017.02.042

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