Nonlinear dynamics and chaos in fractional duffing system

Abstract

Dynamical complexity of a Duffing oscillator in the presence of both a linear and fractional damping and excited harmonically has been investigated. The potential energy term involve in the system comprises two minima i.e., double well potential. Numerical simulation has been carried out with a view to understand the complex dynamics of such a fractional Duffing system with (i) increased values of the fractional order, and (ii) increased value of the amplitude, of the external harmonic excitation while retaining the values of other parameters of the system. Time series, phase portraits have been extensively used to demonstrate pictorially the complex dynamics of the system. In addition, Lyapunov exponents have been computed in each of the cases (i) and (ii) to quantitatively asses the involved dynamical complexity.