Dynamic analysis of fractional-order predator???prey biological economic system with Holling type II functional response

A fractional-order predator???prey biological economic system with Holling type II functional response is proposed. Local stability and Hopf bifurcation of predator???prey systems have been investigated in both commensurate and incommensurate fractional-order systems. We explore how the economic profit and fractional orders influence the local stability and Hopf bifurcation for the fractional-order predator???prey system. For an incommensurate system, we propose a new theory for the existence of Hopf bifurcation when the fractional orders are considered as bifurcation parameters. Several numerical examples are demonstrated to validate the theoretical results