Discretization of forced Duffing system with fractional-order damping

Abstract

In this paper we are interested in studying the effect of the fractional-order damping in the forced Duffing oscillator before and after applying a discretization process to it. Fixed points and their stability are discussed for the discrete system obtained. Finally, numerical simulations using Matlab are carried out to investigate the dynamic behavior such as bifurcation, chaos, and chaotic attractors. We note that on increasing the value of the fractional-order parameter, the resulting discrete system is stabilized.©2014 El-Sayed et al.; licensee Springer.