Analysis of Inter-Spike Interval Characteristics of Piecewise Constant Chaotic Spiking Oscillators

This paper studies dynamics of a simple chaotic spiking oscillator having piecewise constant characteristics. The state variable can vibrate and is reset to the base level just after it reaches the threshold. Repeating this vibrate-and-fire behavior, rich chaotic spike-trains can be generated. Since the solution and return map are piecewise linear, precise analysis is possible. We have investigated characteristics of inter-spike intervals (ISIs) and have found interesting properties: "The system can output chaotic spike-trains characterized by tine-like spectrums of ISIs. Such phenomena and chaos with continuous spectrum appear alternately and make window-like structure in the parameter space. The continuous spectrum of chaos can have wider-band than other types of spiking oscillators." Presenting a simple electric circuit, typical phenomena are confirmed experimentally.