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

2025/05/16 by Adrián Gómez, Gomez, Adrian, Cesar Guayasamin +1
Medicine · Physics and Astronomy · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #stochastic dynamics and bifurcation #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2505.11657

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 < \dfracρδ+H ≤ 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≠ r). The proof combines explicit upper and lower solutions construction with characteristic equation analysis, supported by numerical simulations.

Citations

• Traveling waves in reaction-diffusion equations with delay in both diffusion and reaction terms
• Dirichlet Problem for the Diffusive Nicholson's Blowflies Equation
• An outline of the dynamics of animal populations.

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