Bifurcation analysis of a generalist predator–prey system with fear-induced prey competition, prey refuge and maturation delay

In this paper, we develop a generalist predator–prey model with fear-induced prey competition, carry-over effects, prey refuge, and predator maturation delay. The model reflects findings from biological research, which suggest that predators not only reduce prey populations through direct predation but also indirectly impact prey growth rate by inducing fear and intraspecific competition. For the non-delayed system, the model’s well-posedness, positivity, and boundedness are analyzed, and the emergence and disappearance of coexistence equilibrium points are linked to changes in intraspecific competition and predator’s growth rate. This facilitates the identification of saddle–node and Hopf bifurcations. The theoretical analysis of these bifurcations is further validated through numerical examples. The existence and non-existence of limit cycle at positive equilibrium are investigated by varying prey refuge, fear, and predator’s growth rate. A differential sensitivity analysis highlights that lower fear and carry-over effect parameters result in oscillatory behavior, while lower carry-over effect values stabilize the system. The combined effects of prey competition and predator-induced fear reduces the long-term population levels of both species. When fear becomes strong enough, the system transitions from ongoing cycles to a stable steady state. For the delayed system, very low or high prey’s birth rate lead to stability or instability, respectively, for all time delay values, while moderate birth rate of prey induce multiple stability-instability transitions as time delay increases. Numerical simulations, performed using MATLAB R2021a ode45 and dde23 solvers, confirm the theoretical results.