Analysis of Superstable Phenomena Generated by Piecewise-Constant Chaotic Spiking Oscillator with State-Dependent Switching

Abstract

This paper analyzes the superstable periodic orbits (SSPOs) generated by a piecewise-constant chaotic spiking oscillator. For this oscillator, the oscillation and reset of states are repeated, which generates chaos and SSPOs. A one-dimensional return map described by the dynamics is theoretically derived. This map has discontinuous points. A theoretical analysis of border-collision bifurcations is performed to clarify the regions of the SSPOs in the parameter space.