Bifurcation analysis of a fractional-order delayed rolling mill's main drive electromechanical coupling system (Q2052007)

Summary: This work is focused on a rolling mill's main drive electromechanical coupling system. Firstly, we equip electromechanical coupling system with fractional-order time delay. Secondly, we, respectively, derive the conditions for occurrence of Hopf bifurcation around equilibriums \(E_0(0,0,0,0)\) and \(E_1(x_1^\ast, 0, x_3^\ast, 0)\). It is found that the fractional order \(\alpha\) and time delay \(\tau\) in the system play an important role on the system stability. Finally, numerical simulations are given to verify the analytic results.