In this study, we report an explicit analytical solution of state-controlled cellular neural network (SC-CNN) based second-order nonautonomous system. The proposed system is modeled with an aid of a generalized two-state-controlled cellular neural network (CNN) equations and experimentally realized by imposing a suitable connection of simple two-state-controlled generalized CNN cells following the report of Swathi et al. . The chaotic and quasi-periodic dynamics observed from this system have been investigated through an analytical approach for the first time. The intriguing dynamics observed from the system where further substantiated by phase portraits, Poincaré map, power spectra, and “ test.” We trace the transition of the system from periodic to chaos through analytical solutions, which are in good agreement with hardware experiments. Additionally, we show PSpice circuit simulation results for validating our analytical and experimental studies.