Control of inter-spike-interval density of piecewise-constant chaotic spiking oscillator with dead-time

In this paper, we consider inter-spike-interval (abbr. ISI) density of a chaotic spiking oscillator with piecewise-constant vector field. The system generates various spike trains governed by its chaotic behavior. To study these chaotic spike trains is not only interesting for fundamental nonlinear problems, but also important for engineering applications. First, in order to analyze the behavior of the system, we define 1-D return map and obtain probability distribution of ISI from the invariant measure of the return map. Since the return map is exactly piecewise-linear, the rigorous ISI density can be obtained. Next, we propose the novel method of controlling ISI by using dead-time depends on state variable at the moment of spiking. We show the effectiveness of our proposed method theoretically and demonstrate it in the both of simulations and laboratory measurements.