FRACTAL CHARACTERIZATION OF EVOLVING TRAJECTORIES OF DUFFING OSCILLATOR

This study utilised fractal disk dimension characterization to investigate the time evolution of the Poincare sections of a harmonically excited Duffing oscillator. Multiple trajectories of the Duffing oscillator were solved simultaneously using Runge-Kutta constant step algorithms from set of randomly selected very close initial conditions for three different cases. These initial conditions were from a very small phase space that approximates geometrically a line. The attractor highest estimated fractal disk dimension was first recorded at the end of 15, 22, and 5 excitation periods for Case-1, Case-2 and Case-3 respectively. The corresponding scatter phase plots for Case-1 and Case-2 agreed qualitatively with stroboscopic-ally obtained Poincare sections found in the literature. The study thus established sensitivity of Duffing to initial conditions when driven by different combination of damping coefficient, excitation amplitude and frequency. It however showed a faster, accurate and reliable alternative computational method for generating its Poincare sections. [PUBLICATION ABSTRACT]