A complete dynamical analysis of a discontinuously driven resonance circuit

Multistable systems with non-smooth dynamics provide serious challenges to the engineering design. Using a suite of standard numerical tools, our analysis of a canonical non-smooth system: a resonant circuit with an asymmetric cubic restoring force fed by a discontinuous square wave voltage, offers two important contributions to the study of such systems. First, the discontinuous forcing itself causes the basins of attraction with riddled boundaries to be created, which is a fundamental sensitivity that cannot be predicted by local analysis. Second, our Lyapunov landscape analysis finds the coefficient of quadratic nonlinearity, l 2 , to be a significant critical stability switch, which can be directly used to control the predictability of the system. Lastly, we prove this control by achieving chaos synchronization and determining the critical coupling necessary to stabilize a problem stabilize synchronously as the required. This description of the global dynamics of the system is crucial for achieving robust performance in systems that incorporate both electronic and mechanical components.