Heteroclinic Connection in a Nicholson's delayed model with Harvesting term

Adrian Gomez; Cesar Guayasamin

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arXiv · 2505.11657

Heteroclinic Connection in a Nicholson's delayed model with Harvesting term

Adrian Gomez·Cesar Guayasamin

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Abstract

In this paper we prove the existence of monotone heteroclinic solutions for the delayed Nicholson's blowflies model with harvesting: \[ x'(t) = -\delta x(t) - Hx(t-\sigma) + \rho x(t-r)e^{-x(t-r)}. \] Under the condition $1 < \dfrac{\rho}{\delta+H} \leq e$, we establish the connection between the equilibria $0$ and $\ln(\rho/(\delta+H))$ using the Wu and Zou monotone iteration method adapted for two delays ($\sigma \neq r$). The proof combines explicit upper and lower solutions construction with characteristic equation analysis, supported by numerical simulations.

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Adrian Gomez, Cesar Guayasamin. 2025-05-16. Heteroclinic Connection in a Nicholson's delayed model with Harvesting term. https://arxiv.org/abs/2505.11657

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