Nonlinear dynamics of a Darwinian Ricker system with strong Allee effect and immigration

Karima Mokni, Halima Ben Ali, Bapan Ghosh and Mohamed Ch-Chaoui

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 229, issue C, 789-813

Abstract: In this paper, we investigate the complex dynamics of a Darwinian Ricker system through a comprehensive qualitative and dynamical analysis. Our research shows that the system exhibits Neimark–Sacker bifurcation, period-doubling bifurcation, and codimension-two bifurcations associated with 1:2, 1:3, and 1:4 resonances. These findings are derived using bifurcation and center manifold theories. We numerically illustrate all bifurcation results and chaotic features, providing a thorough understanding of the system’s behavior. This detailed examination of the Darwinian Ricker system, with a focus on the interplay between immigration and the strong Allee effect, enhances our understanding of the intricate mechanisms driving population dynamics. Furthermore, it highlights the significant implications for ecological modeling, particularly in predicting ecosystem responses to external perturbations such as climate change and species invasions.

Keywords: Asymptotic stability; Evolutionary game theory methodology; Bifurcations analysis; Immigration and Allee effect (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:229:y:2025:i:c:p:789-813

DOI: 10.1016/j.matcom.2024.10.017

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