Dynamic complexities in a predator–prey model with prey refuge influenced by double Allee effects

Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty and Renji Han

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 227, issue C, 527-552

Abstract: Within the context of a two-dimensional framework encompassing interacting species, an examination is conducted in this study on the double Allee effect and prey refuge, considering both species in the interaction. The stability of the feasible equilibrium of the system and diverse bifurcation patterns including codimension-one and codimension-two bifurcations are scrutinized through theoretical and numerical investigations, which reveals the complex dynamics induced by saturated functional response and double Allee effects. Additionally, one-parameter bifurcation diagrams and two-parameter bifurcation diagrams are constructed to intricately evaluate the system’s dynamics indicative of the presence of multiple attractors like bi-stability and tri-stability. Lastly, the sensitivity analysis is performed to delve into the effect of system parameters on species density, which indicates that the parameter η proportional to the conversion rate is the most sensitive parameter. A brief discussion further reveals that the model without double Allee effect reduces dynamic complexity.

Keywords: Interacting species; Double Allee effect; Codimension-one and -two bifurcations; Norm forms; Homoclinic and heteroclinic trajectories; Sensitivity analysis (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:227:y:2025:i:c:p:527-552

DOI: 10.1016/j.matcom.2024.08.015

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