Dynamic analysis of piecewise nonlinear systems with fractional differential delay feedback control

Abstract

This paper mainly analyzes a class of piecewise nonlinear systems with fractional differential delay feedback control. The average method is used to solve the nonlinear system to obtain the amplitude-frequency relationship of the system. The analytical solution of the system can quantitatively analyze the system. At the same time, the correctness of the analytical solution of the system is verified by numerical solution. The effects of linear damping, linear stiffness and nonlinear stiffness of the system and the proportion, fractional order coefficient and fractional order number of the feedback controller on the amplitude-frequency characteristics of the system are analyzed. Finally, the dynamic analysis of the system is carried out. Taking the fractional order coefficient as the bifurcation parameter, the global characteristics of the bifurcation diagram, time history diagram and phase diagram system under different parameter perturbations are studied by power series expansion method. It is found that the system exhibits periodic motion, period doubling motion and chaos with the change of perturbation parameters.