Complicated superstable periodic behavior in piecewise constant circuits with impulsive excitation

Abstract—This paper studies piecewise constant circuits with an impulsive switch. Since vector field of the circuit equation is piecewise constant, the trajectories are piecewise linear : it is well suited for precise analysis. First, we consider the autonomous case. The switch is controlled by a state and the circuits can exhibit chaotic behavior. Second, we consider the non-autonomous case. The switch is controlled by time and the circuits can exhibit rich super stable periodic behavior. We have confirmed the behavior in numerical simulations and embedded return maps have a flat part. Typical phenomena can be confirmed experimentally.