Harvesting-induced bifurcation and memory-driven stability in a fractional-order predator-prey model with Beddington-DeAngelis functional response

Abstract

This paper develops a fractional-order ecological model describing one prey and two predator species with harvesting, predator interference, and a Beddington-DeAngelis functional response. Caputo fractional derivatives are incorporated to capture memory effects in population dynamics. The model admits a biologically feasible equilibrium and preserves positivity and boundedness. Local stability is established using Matignon's criterion, revealing a memory-induced stability switch and a critical fractional order beyond which the coexistence equilibrium loses stability. For the integer-order case, harvesting-induced bifurcations, extinction thresholds, and Hopf bifurcation points are determined numerically using MATLAB. Numerical simulations demonstrate that fractional-order memory and predator interference jointly enhance system stability and delay harvesting-induced oscillations and population collapse. These findings highlight the important role of memory and interference mechanisms in promoting ecological resilience under sustained harvesting.