[MS10] Model Bifurcations and Ecological Relevance

[MS10-01] Exploring the Existence of Limit Cycle in Predator-Prey Model with Allee Effect and Cannibalism

*Asep Kuswandi Supriatna¹, Maya Rayungsari^1,2, Icih Sukarsih³ (1. Universitas Padjadjaran (Indonesia), 2. Universitas PGRI Wiranegara (Indonesia), 3. Universitas Islam Bandung (Indonesia))

Keywords:

Predator-prey model,Allee effect,Cannibalism

The Allee effect describes a phenomenon where a population experiences reduced per capita growth rates at low densities due to various biological and ecological factors. The interplay between predator-prey dynamics and ecological factors, such as the Allee effect and cannibalism, could influence population stability and oscillatory behavior. In this study, we analyze the existence of a limit cycle in a predator-prey system governed by a Holling Type II functional response, incorporating either an Allee effect or cannibalism in the population. The model exhibits rich dynamical behavior, including bistability, Hopf bifurcation, and potential homoclinic bifurcations. Through phase plane analysis and bifurcation diagrams, we identify conditions under which a stable limit cycle emerges, leading to sustained oscillations in predator and prey populations. We explore the role of predator mortality, cannibalism, and Allee threshold in shaping system stability and discuss the ecological implications of our findings. Our results highlight the critical balance between predation pressure and prey population thresholds in maintaining coexistence and oscillatory dynamics. The properties generalize to the model with fuzzy parameters and initial conditions. This presentation provides insights into how small changes in ecological parameters can lead to drastic shifts in population behavior, offering valuable perspectives for theoretical ecology and conservation strategies.