Analysis of a Quantized Chaotic System

We consider quantized chaotic dynamics for a spiking oscillator with two periodic inputs. As the first input is applied, the oscillator generates various periodic and chaotic pulse-trains governed by a pulse position map. As the second input is added, the oscillator produces pulse positions restricted on a lattice, and the pulse position map is quantized. Then the oscillator generates a set of super-stable periodic pulse-trains (SSPTs). The oscillator has various coexisting SSPTs and generates one of them depending on the initial state condition. In order to characterize the set of SSPTs, we elucidate the number and the minimum pulse interval of the SSPTs theoretically. By presenting a simple test circuit, we then verify some typical phenomena in the laboratory environment.