Study on a fractional order delayed predator-prey model including prey refuge and type II functional response

The fractional-order delayed predator-prey dynamical scheme studied here includes a prey refuge with Holling type-II functional response. The existence and uniqueness of a solution for our scheme are explored. Hopf bifurcation with respect to delay is reconnoitered, besides local and global stability of existing steady states of fractional order0 < q ≤ 1. It is discovered that the delay passes through a series of crucial values when Hopf bifurcation takes place. Additionally, both theoretically and statistically, the impacts of prey refuge effects and fractional order on system stability are investigated. The delayed differential scheme's dynamics and results durability are improved by fractional order. Fractional order enhances the stability of the solutions and enriches the dynamics of the delayed differential model. Additionally, both theoretically and by the use of numerical simulations, the effects of fractional order and the prey refuge effects on the stability of the system are investigated. © 2023 The Author(s)