FRACTAL CHARACTERIZATION AND COMPARISON OF CHAOS IMPACT OF EXCITED DUFFING OSCILLATOR PARAMETERS

This study adopted two popular Runge-Kutta algorithms to investigate the chaotic driven impact of two important parameters of excited Duffing oscillator using fractal disk dimension characterization and comparison. The constant time step simulation of 'family' of Duffing oscillator beyond unsteady periods was employed to create scatter phase plots at every end of excitation period and over one thousand consecutive excitation periods. The resulting distorted Poincare images were quantified using fractal disk dimension obtained by use of optimum disk count method. However, the comparison of dimension distribution was made on one hundred equal intervals between limits for two distinct cases. The spectrum of estimated fractal disk dimension is noisy. Its variation is 1.312 less than or equal to D less than or equal to 1.681 and 1.126 less than or equal to D less than or equal to 1.358 respectively for damp and excitation amplitude based cases using fourth order Runge-Kutta algorithms as simulation tool. However the variation of dimension is 1.277 less than or equal to D less than or equal to 1.688 and 1.140 less than or equal to D less than or equal to 1.384 for corresponding case using fifth order Runge-Kutta algorithms. Furthermore, both cases enjoyed unimodal disk dimension distribution for all simulation algorithms. The approximated modal dimension is 1.52 and 1.23 in favour of damp and excitation amplitude value while the average modal relative frequency is 8.0%.The study results therefore supported damp parameter properly tune as easier agent of impacting chaotic behaviour in Duffing oscillator compares with its excitation amplitude counterpart other simulation conditions remains same.