Antiperiodic oscillations in a forced Duffing oscillator

Regularity has always been attributed to periodicity. However, there has been a spurt of interest in another unique type of regularity called anitperiodicity. In this paper we have presented results of antiperiodic oscillations obtained from a forced duffing equation with negative linear stiffness wherein the increase in the number of peaks in antiperiodic oscillation with the forcing strength has been observed. Similarity function has been used to identify the antiperiodic oscillation and further the bifurcation diagram has been plotted and stability analysis of the fixed points have been carried out to understand its dynamics. An analog electronic circuit governed by the forced Duffing equation has been designed and developed to investigate the dynamics of the antiperiodic oscillations. The circuit is quite robust and stable to enable the comparison of its analog output with the numerically simulated data. Power spectrum analysis obtained by fast Fourier transform has been corroborated using a nonlinear statistical technique called rescale range analysis method. By this technique we have estimated the Hurst exponents and detected the coherent frequencies present in the system.