Investigation of Poincare Solutions of Nonlinear Duffing and Pendulum under Selected Periodic Excitations Using Fractal Disk Characterisation

Literature has shown that harmonically excited nonlinear Duffing and pendulum oscillators can respond chaotically under the influence of some their drive parameters combination. However, literature is scarce on steady state responses these when arbitrarily periodically. Therefore, this research was designed to investigate potential qualitative quantitative variation in Poincare solutions selected periodic excitations compared counterparts. The non-dimensional second Order Differential Equation (ODE) corresponding respectively governing equations for harmonically/periodically were solved using constant step fourth order Runge-Kutta algorithms. obtained characterised by visual inspection fractal dimension measure disk counting method. Visual show they are qualitatively indistinguishable. estimated varied significantly. absolute found be between 1.37% 4.92% oscillator 5.67% 7.39% oscillator.