Analysis of the stability of a predator-prey model including the memory effect, double Allee effect and Holling type-I functional response

• DOI: 10.1371/journal.pone.0305179
• Publication Date: 2025-01-03T18:22:13Z
• Authors: Ramesh K.; Ranjith Kumar G.; Aziz Khan; Thabet Abdeljawad
• Keywords: Allee effect; Equilibrium point

This study proposes and analyses a revised predator-prey model that accounts for twofold Allee impact on the rate of prey population expansion. Employing Caputo fractional-order derivative, we account memory suggested model. We proceed to examine significant mathematical aspects model, including uniqueness, non-negativity, boundedness, existence solutions noninteger order system. Additionally, all potential equilibrium points strong weak effect are examined under Matignon’s condition, along with current state conditions local stability analysis. Analytical results also provided necessary circumstances Hopf bifurcation initiated by fractional derivative occur. demonstrated global asymptotic positive point in both cases selecting an appropriate Lyapunov function. study’s innovation is its comparative investigation effects. To conclude, numerical simulations validate theoretical findings provide means investigate system’s more dynamical behaviours.