A nonlinear mathematical model on the dynamical study of a fractional-order delayed predator–prey scheme that incorporates harvesting together and Holling type-II functional response

Abstract

In the present investigation, the functional response of Holling type II and the impact of harvesting together are used to analyse the dynamical behaviour of a fractional-order delayed predator–prey scheme. In addition to the existence and uniqueness of the solution, the suggested design’s boundedness has also been proven. Additionally, both locally and globally applicable stability criteria for each feasible equilibrium point as well as their requirements for existence were also looked into. The Magtinon’s statement is used to obtain the local stability conditions, and the creation of an adequate Lyapunov function is used to demonstrate the global stability. Furthermore, we discussed about the potential for a Hopf bifurcation close to a given interior point while considering the delay to be a bifurcation factor. The Predictor–Corrector system is then put to use to carry out certain numerical simulations. Fractional order enhances the stability of the solutions and enriches the dynamics of the delayed differential system with harvesting. Our study reveals that delayed fractional order includes harvesting with type-II functional control can be used to adjust the biomass of prey species and predator species such that prey species and predator species finally each a better state level.

Keywords

• Fractional order
• Predator–prey model
• Time delay
• Stability
• Harvesting
• Hopf-bifurcation