Simulating the Influence of Time Delay on Fractional Differential Equations based on Predictor-Corrector Scheme

Abstract

This paper aims to investigate a fractional order prey predator model with group defense and time delay through differential equation linearization theory and predictor-corrector scheme. In this model, we use the Holling-IV functional response, called Monod-Haldane function, for interactions between prey and predator species. Firstly, the uniqueness of the solution to the initial value problem of this system are proved. Secondly, the existence of equilibrium points is discussed, and the Hopf bifurcation of this system is studied using time lag as the bifurcation parameter. Finally, based on the predictor-corrector scheme, we conduct numerical simulations with corresponding parameters and different time delay parameters to analyze the impact of time delay on dynamics.