Work

A Degenerate Bifurcation Perspective on High Sensitivity in a Modified Gower-Leslie Model with Additive Allee Effect

Year: 2025

Type: preprint

Abstract: The population dynamics in a modified Leslie-Gower model with an additive Allee effect are highly sensitive to both parameters and initial population densities, leading to outcomes ranging from coextinction to sustained multistable steady states. This work links this sensitivity to complicated bifurcations. We establish the existence of a codimension 4 nilpotent cusp and a corresponding degenerate Bogdanov-Takens bifurcation with codimension 4, which critically shape the system's response to parameter changes. Most significantly, we prove that the Hopf bifurcation occurring at a center-type equilibrium can give rise to up to five limit cycles-a phenomenon scarcely documented in previous ecological studies-thereby inducing a pronounced dependence of oscillatory regimes on initial conditions. Numerical simulations confirming heteroclinic loops and multiple limit cycles provide consistent support for the theoretical analysis.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.09126

Authors: Wang, Xiaoling, Wu, Kuilin, Zou, Lan

Institutions: Guizhou University, Guiyang University, Capital Normal University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Science and Technology Program of Guizhou Province

Awards: G7837625050, G7892882979, G8054864772

OpenAlex ID: W6929540274

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