Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense

Manoj Kumar Singh, Arushi Sharma and Luis M. Sánchez-Ruiz ()
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Manoj Kumar Singh: Department of Mathematics and Statistics, Banasthali Vidyapith, Tonk 304022, India
Arushi Sharma: Department of Mathematics and Statistics, Banasthali Vidyapith, Tonk 304022, India
Luis M. Sánchez-Ruiz: Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2025, vol. 13, issue 4, 1-19

Abstract: The Allee effect and group defense are two naturally occurring phenomena in the prey species of a predator–prey system. This research paper examines the impact of integrating the Allee effect on the dynamics of a predator–prey model, including a density-dependent functional response that reflects the defensive strategies of the prey population. Initially, the positivity and boundedness of the solutions are examined to ascertain the biological validity of the model. The presence of ecologically significant equilibrium points are established, followed by examining parametric restrictions for the local stability to comprehend the system dynamics in response to minor perturbations. A detailed computation encompasses diverse bifurcations, both of codimension one and two, which provide distinct dynamic behaviors of the model, such as oscillations, stable coexistence, and potential extinction scenarios. Numerical simulation has been provided to showcase complex dynamical behavior resulting from the Allee effect and prey group defense.

Keywords: predator–prey model; stability; bifurcation; multiplicative Allee effect; group defense (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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