Nonlinear dynamics of Duffing system with fractional order damping

Nonlinear dynamics of Duffing system with fractional order damping is investigated. The equations of fractional order damped Duffing system are established. The four-order Runge-Kutta method and ten-order CFE-Euler methods are performed to solve the fractional order Duffing equations. The effects of fractional order on the system dynamics are proposed with phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is utilized to analyze the effect of excitation amplitude and frequency on Duffing system with fractional order damping. The analysis shows that the fractional order damped Duffing system exhibits period motion, chaos, period motion, chaos, period motion one by one when the fractional order change from 0.1 to 2.0. A period doubling route to chaos is appeared clearly. The numerical results verify the significant effect of fractional order on system dynamics. It is necessary to consider the fractional order of damping in the design and analysis of system dynamics.