Bifurcation analysis of delayed predator–prey system with fear effect, additional food for predator, prey refuge and predator age structure

In this paper, we construct a predator-prey model that includes fear, prey refuge, anti-predator behavior, predator age structure, and additional food. We examine certain basic properties of the system, such as positivity and uniformboundedness. Additionally, we study the conditions for the existence and stability of all equilibrium points, and obtainthe conditions and threshold values for local bifurcations triggered by various parameters through computations (fear, refuge coefficient, food quantity, juvenile predator coefficient and natural mortality rate of predator). Following that, we investigate the influence of all combinations of delay factors (fear on the prey's growth rate and gestation period of the predator population) on the stability of the proposed system. Finally, we performed numerical simulations to validate our theoretical research results and provide a detailed understanding of the influences of these parameters on the dynamics of the system. The results indicate that fear, prey refuge, additional food, and age structure distribution all play a key role in population stability. Mathematics Subject Classification (2010). 34C23; 92D25.