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

Abstract

In this paper we prove the existence of monotone heteroclinic solutions for the delayed Nicholson's blowflies model with harvesting: \[ x'(t) = -δx(t) - Hx(t-σ) + ρx(t-r)e^{-x(t-r)}. \] Under the condition $1<\frac{\rho }{\delta +H}\le e$, 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 ($\sigma \ne r$). The proof combines explicit upper and lower solutions construction with characteristic equation analysis, supported by numerical simulations.

arXiv comment25 pages, 5 figures. Submitted to Journal of Mathematical Biology. Contains numerical simulations of heteroclinic solutions for a Nicholson's model with two delays (sigma not equal to r ) and harvesting term