Paired asymmetric periodic oscillations in a pair of first-order asymmetric nonlinear circuit systems

In this paper, the analytical solutions for paired asymmetric periodic oscillations in a pair of first-order asymmetric nonlinear circuit systems are developed for the first time. The purpose of this study is to show the paired asymmetrical nonlinear oscillations existing in paired asymmetric nonlinear systems. Such analytical solutions in nonlinear systems can be realized through the nonlinear circuit systems. Thus, the paired nonlinear electrical circuits are established for the experimental study of the periodic oscillations. The analytical paired asymmetric periodic oscillations are regenerated experimentally through the paired nonlinear electrical circuits. The analytical and experimental periodic oscillations match very well. The accurate analytical solutions of periodic oscillations are given herein in time and frequency domains. To consider excitation effects on periodic oscillations in such 1-dimensional nonlinear circuit systems, the asymmetric periodic oscillations varying with excitation amplitudes for the nonlinear circuit are presented through harmonic amplitudes, and the corresponding stability and bifurcations of such paired asymmetric periodic oscillations are determined through eigenvalue analysis. Such studies provide a theoretic base to design the nonlinear circuit devices or cells. From the analytical solutions, the experimental and numerical results are carried out for comparison to the analytical results. Such 1-dimensional first-order nonlinear electrical circuit devices can be designed for extensive applications in industry.