Positive periodic solutions for discrete Nicholson system with multiple time-varying delays

Xinning Niu; Huixin Liu; Dan Li; Yan Yan; Xinning Niu; Huixin Liu; Dan Li; Yan Yan

doi:10.3934/era.2023354

Electronic Research Archive

2023, Volume 31, Issue 11: 6982-6999. doi: 10.3934/era.2023354

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Research article

Positive periodic solutions for discrete Nicholson system with multiple time-varying delays

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 06 July 2023 Revised: 10 October 2023 Accepted: 18 October 2023 Published: 31 October 2023

Fly communities exhibit rich ecological dynamics, and one of the important influencing factors is the interaction between species. A discrete Nicholson-type system with multiple time varying delays which considers the mutualism relationship between two fly species is investigated in this paper. Sufficient conditions for the existence of positive periodic solutions are elucidated. The result is obtained by the well-known continuation theorem of coincidence degree theory. An example is attached to illustrate our result. Moreover, the actual biological descriptions obtained from our main result are explained.
- discrete Nicholson system,
- mutualism relationship,
- positive periodic solution,
- time-varying delay,
- continuation theorem of coincidence degree theory
Citation: Xinning Niu, Huixin Liu, Dan Li, Yan Yan. Positive periodic solutions for discrete Nicholson system with multiple time-varying delays[J]. Electronic Research Archive, 2023, 31(11): 6982-6999. doi: 10.3934/era.2023354

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Abstract

Fly communities exhibit rich ecological dynamics, and one of the important influencing factors is the interaction between species. A discrete Nicholson-type system with multiple time varying delays which considers the mutualism relationship between two fly species is investigated in this paper. Sufficient conditions for the existence of positive periodic solutions are elucidated. The result is obtained by the well-known continuation theorem of coincidence degree theory. An example is attached to illustrate our result. Moreover, the actual biological descriptions obtained from our main result are explained.

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