Heteroclinic Connection in a Nicholson's delayed model with Harvesting term
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912380834807808 |
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| author | Gomez, Adrian Guayasamin, Cesar |
| author_facet | Gomez, Adrian Guayasamin, Cesar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heteroclinic Connection in a Nicholson's delayed model with Harvesting term Gomez, Adrian Guayasamin, Cesar Dynamical Systems 34K26 (Primary), 34K20, 92D25, 34K12, 34K19 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. |
| title | Heteroclinic Connection in a Nicholson's delayed model with Harvesting term |
| topic | Dynamical Systems 34K26 (Primary), 34K20, 92D25, 34K12, 34K19 |
| url | https://arxiv.org/abs/2505.11657 |