Dynamic analysis of a fractional-order predator–prey model with harvesting

In this paper, we have investigated the effect of the fractional-order derivative in a predator–prey model with combined harvesting. Fractional-order derivative is more suitable than integer-order derivative where memory effect occurs. We have established the solution’s existence, uniqueness, non-negativity, and boundedness for the fractional system. Furthermore, the local stability has been discussed using Matignon’s condition and the global stability is established by constructing a suitable Lyapunov function. Further, we have discussed the existence condition of Hopf bifurcation considering the order of derivatives as a bifurcation parameter. Finally, the effect of the predator harvesting rate on the prey–predator dynamics is examined. Numerical simulations demonstrate the validity of the obtained theoretical results, the impact of different parameters, and combined harvesting on the fractional-order predator–prey dynamics using the Adams–Bashforth–Moulton type predictor–corrector scheme and MATLAB software. Also, the significance of combined harvesting over selective harvesting has been discussed in the numerical section.