Control of Hopf bifurcation for a four-dimensional fractional order hyperchaotic system with coexisting attractors

In this work, a four-dimensional fractional order hyperchaotic system with coexisting attractors is excogitated. The stability analysis of the equilibrium point is investigated, and the chaotic and hyperchaotic behavior of the system is well demonstrated numerically by the Lyapunov exponents. By applying delayed feedback control technique, we obtain the existence condition of Hopf bifurcation for the such system. Some numerical simulations are exhibited to substantiate the obtained results in the end, which also displays some interesting dynamical phenomena, such as quasi-periodic, and hyperchaotic. The work reveals that the fractional order and delays have a great significance to controlling the hyperchaotic system.