Dynamical analysis of a discrete fractional order prey-predator system incorporating a prey refuge with Holling type II response

In this present work, a class of Fractional Order Predator-Prey System (FOPP) in discrete time with Holling type II functional response incorporating a prey refuge of the form x ( i + 1 ) = x ( i ) + h v Γ ( 1 + v ) [ r x ( i ) − r x 2 ( i ) − a ( ( 1 − μ ) x ( i ) ( 1 − μ ) x ( i ) + b ) y ( i ) ] y ( i + 1 ) = y ( i ) + h v Γ ( 1 + v ) [ − c y ( i ) + d ( ( 1 − μ ) x ( i ) ( 1 − μ ) x ( i ) + b ) y ( i ) ] is considered. The stability of the proposed system is discussed by analyzing the characteristic equation at the equilibrium points along with the existence, uniqueness, non-negativity and boundedness of the solutions. Theoretical findings are supported by numerical examples and enhanced by pictorial representations such as time series, bifurcation diagrams and phase portraits.