Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and effect fear with Holling type II functional response. The arises from study biological system involving arctic foxes (predator), lemmings (prey), seal carcasses (subsidy). positivity asymptotically uniform boundedness solutions have been derived. Analytically, we studied criteria for feasibility stability different equilibrium points. addition, derived sufficient conditions existence local bifurcations codimension 1 (transcritical Hopf bifurcation). It also observed that there some time lag between perceiving predator signals through vocal cues reduction prey’s birth rate. So, analyzed dynamical behaviour delayed model. Numerical computations performed using MATLAB validate all analytical findings. Numerically, it has predator, prey, subsidy can always exist at nonzero input But, high rate, population cannot persist huge growth due availability food sources.