Bifurcation analysis of fractional duffing system based on improved short memory principle method

Abstract

In this paper, the dynamic characteristics of fractional Duffing system are analyzed and studied by using the improved short memory principle method. This method has small amount of calculation and high precision, and can effectively improve the problem of large amount of calculation caused by the memory of fractional order. The influence of frequency change on the dynamic performance of the fractional Duffing system is studied using nonlinear dynamic analysis methods, such as Phase Portrait, Poincare Map and Bifurcation Diagram. Moreover, the dynamic behaviour of the fractional Duffing system when the fractional order and excitation amplitude changes are investigated. The analysis shows that when the excitation frequency changes from 0.43 to 1.22, the bifurcation diagram contains four periodic and three chaotic motion regions. Periodic motion windows are found in the three chaotic motion regions. It is confirmed that the frequency and amplitude of the external excitation and the fractional order of damping have a greater impact on system dynamics. Thus, attention shall be paid to the design and analysis of system dynamics.