The impact of fear and refuge on the dynamics of predator-prey model: Stability and simulation

In this work, it was proposed and researched to use a mathematical model to simulate the interaction between two preys and two predators, such that the first prey will feel the fear of predation and the need for shelter, and this depends on the predators. The presence and stability of all possible equilibrium points was chosen when possible. The appropriate Lyapunov function is used to show the general stability of the balance points. The stability requirements of the system were determined. Numerical simulations were performed to validate the long-term behavior obtained for the model and understand the effects of the main parameters of the model in order to confirm our analytical conclusions.