 On the stability of a single-species model with a generic delay distribution kernelIsam Al-Darabsah Chaos, Solitons & Fractals, 2024, vol. 187, issue C Abstract: The delayed logistic equation, also known as Hutchinson’s equation, is a simple and elegant model commonly used to capture critical features of complex phenomena in biology, medicine, and economics. This paper studies the stability of a single-species logistic model with a general delay distribution and a constant inflow of nutritional resources. We provide conditions for the linear stability of the positive equilibrium and the occurrence of Hopf bifurcation. The findings complement existing literature and are applied to specific delay distributions: Uniform, Dirac-delta, and gamma distributions. Without resource inflow, we find that the positive equilibrium is stable for short delays but loses stability through Hopf bifurcation as the mean delay increases. The model’s dynamics vary with resource inflow based on the delay distribution: in uniform and Dirac-delta distributions, the dynamics are similar to the no-inflow case, whereas for the gamma distribution, stability depends on the delay order p=1,2,3. Keywords: Single-species model; Hopf bifurcation; Distributed delay (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009779 DOI: 10.1016/j.chaos.2024.115425 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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