The Stabilizing mechanism for an interrupted dynamical system with periodic threshold

Abstract

This study mathematically analyzes an interrupted dynamical system (IDS) with a periodic threshold. First, we describe a simple IDS, which is dependent on its own state and a periodic interval, and explain the behavior of the waveform. Then, we define the discrete map (return map) of the system and calculate the bifurcation diagrams. Finally, we focus on the dynamical structure of the return map in the system with a periodic threshold and discuss the stabilizing mechanism, especially its effect in a wide parameter space. The stabilizing effect is verified by the laboratory experiment.