A Fractional-Order Food Chain System Incorporating Holling-II Type Functional Response and Prey Refuge

Recently, many scholars have focused on the applications of the fractional derivatives and fractional calculus. Compared with the integer-order differential equations, the momentous advantage of a fractional-order system is that it has memory. The introduction of fractional differential equation solves the problem of time memory, which makes the fractional ecosystem more reasonable than the ordinary differential ecosystem. Thus, more and more reports on fractional-order two species model and fractional-order food chain system of three species have been presented in the past decade. The study on fractional-order biological systems also involves the existence of solutions, boundedness of solutions, stability of equilibrium point, bifurcation, and chaos. It is different from the integer-order ecosystem that the chaos may occur in ecosystem with orders less than 3.