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Mon. Jul 7, 2025

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Asymptotic and short-term responses of perturbation: A mathematical comparison of stability measures

For over a century, the development of mathematical models and exploring their dynamics have been central to scientific research. In recent years, this field has been significantly enriched by contributions from researchers across multiple disciplines. This mini-symposium aims to provide a comprehensive understanding of model-based ecological principles by introducing several novel population models. These models incorporate various ecological phenomena, including the Allee effect, hunting cooperation, strong-weak competition, Conser functional response, omnivory, age structure, diffusion, and time delays. A notable challenge in the stability analysis of some models arises from the presence of an infinite number of eigenvalues. We demonstrate how the dominant eigenvalue determines population distribution and identify key parameters influencing system behavior. Furthermore, we investigate several bifurcations at equilibrium, including saddle-node, transcritical, pitchfork, and Hopf bifurcations. The discussion also extends to saddle-node bifurcations of limit cycles and rate-induced phase tipping (RP-tipping) between two stable limit cycles. All bifurcations are analyzed within the framework of ecological principles, providing valuable insights into the optimal utilization of biological resources and the maintenance of ecological balance.

Model Bifurcations and Ecological Relevance

Joint Meeting of Asian Conference for Mathematical Biology and Annual Meeting of Japanese Society for Mathematical Biology (ACMB-JSMB2025)

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[MS10-02]Asymptotic and short-term responses of perturbation: A mathematical comparison of stability measures

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