Heteroclinic Connection in a Nicholson's delayed model with Harvesting term
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 $1 < \dfracρ{δ+H} \leq e$, we establish the connection between the equilibria $0$ and $\ln(ρ/(δ+H))$ using the Wu and Zou monotone iteration method adapted for two delays ($σ\neq r$). The proof combines explicit upper and lower solutions construction with characteristic equation analysis, supported by numerical simulations.
math.DS↗