APPLICATION OF AVERAGE POSITIVE LYAPUNOV IN ESTIMATION OF CHAOTIC RESPONSE PEAK EXCITATION FREQUENCY OF HARMONICALLY EXCITED PENDULUM

The drive parameters space of harmonically excited pendulum consist of mix parameters combination leading to different dynamics phenomena is a strong motivation for this study and aims at estimating the peak frequency that favour chaotic response. The simulation of pendulum and estimation of the average Lyapunov exponents by Grahm Schmidt Orthogonal rules at parameter nodal points selected from damp quality, excitation amplitude and drive frequency were effected using popular constant time step Runge-Kutta schemes, RK4, RK5 and RK5B, from two initial conditions through transient and steady periods. The impact of resolution on the measure of percentage of parameters combination leading to chaotic response (PPCLCR) was examined at different resolution levels for increasing drive frequency. The estimated peak frequency is the same across studied resolutions, initial conditions and Runge-Kutta schemes. The peak value of PPCLCR is 69.5, 69.4 and 69.4 respectively for RK4, RK5 and RK5B at initial conditions.