Stability and Hopf Bifurcation of a Delayed Fractional Plankton-Fish System with Incommensurate Orders

In this paper, the issue of stability and Hopf bifurcation of a delayed fractional plankton-fish system with incommensurate orders is investigated. By selecting the time delay as the bifurcation parameter, the associated characteristic equation is analyzed. Then the explicit conditions of stability and Hopf bifurcation are determined. Through theoretical and numerical simulation, it is revealed that time delay has important influence on dynamics of the system. When it greater than the critical value, the proposed system becomes unstable and Hopf bifurcation occurs. In addition, it is further found that various fractional orders have different impact on bifurcation, one of these orders has little impact on Hopf bifurcation.