Existence of periodic solution of Nicholson-type system with nonlinear density-dependent mortality

Ossandón, Gustavo; Sepúlveda, Daniel

doi:10.48550/arxiv.2001.10522

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“…In a recent work from Ossandon and Sepúlveda [18], they prove the existence of positive solutions of periodic variants of (3) by the means of topological methods.…”

Section: Introductionmentioning

confidence: 99%

On persistence of a Nicholson-type system with multiple delays and nonlinear harvesting

Amster¹,

Bondorevsky²

2021

Preprint

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An N -dimensional generalization of Nicholson's equation is analyzed. We consider a model including multiple delays, nonlinear coefficients and a nonlinear harvesting term. Inspired by previous results in this subject, we obtain sufficient conditions to guarantee strong and uniform persistence. Furthermore, under extra suitable hypotheses we prove the existence of T -periodic solutions and, reversing the prior conditions in a convenient manner, we show that the zero is a global attractor.

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“…In a recent work from Ossandon and Sepúlveda [18], they prove the existence of positive solutions of periodic variants of (3) by the means of topological methods.…”

Section: Introductionmentioning

confidence: 99%

On persistence of a Nicholson-type system with multiple delays and nonlinear harvesting

Amster¹,

Bondorevsky²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Existence and exponential stability of periodic solutions of Nicholson-type systems with nonlinear density-dependent mortality and linear harvesting

Ossandón

Sepúlveda

2023

Electron. J. Qual. Theory Differ. Equ.

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In this work we study a Nicholson-type periodic system with variable delay, density-dependent mortality and linear harvesting rate. Using the topological degree and Lyapunov stability theories, we obtain sufficient conditions that allow us to demonstrate the existence of periodic solutions for the Nicholson-type system and, under suitable conditions, the uniqueness and local exponential stability of the periodic solution is established. We illustrate our results with an example and numerical simulations.

show abstract

Existence of periodic solution of Nicholson-type system with nonlinear density-dependent mortality

Cited by 2 publications

References 11 publications

On persistence of a Nicholson-type system with multiple delays and nonlinear harvesting

On persistence of a Nicholson-type system with multiple delays and nonlinear harvesting

Existence and exponential stability of periodic solutions of Nicholson-type systems with nonlinear density-dependent mortality and linear harvesting

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