Resonance phenomenon of interspike intervals from a spiking oscillator with two periodic inputs

We consider a spiking oscillator to which two periodic and synchronized inputs can be applied. As either input is applied, typical phenomena from the oscillator are phase locking and quasi-periodic behaviors. Applying both inputs and adjusting their parameters appropriately, the system behavior approaches a resonance point characterized by: (1) The state is quasi-periodic; (2) the output pulse-train is periodic; and (3) they are not synchronized with the periodic inputs. Generating such resonance phenomena is impossible in the single input case. We present a simple implementation method of the spiking oscillator and verify the typical phenomena in the laboratory.

I. Introduction

In this paper, we consider an oscillator to which multiple inputs can be applied. The multiple-inputs system would exhibit more interesting phenomena than single input systems. As a fundamental problem, it is important to recognize proper phenomena in the multiple-inputs system. It is also important to recognize basic functions of each input. If these functions can be fused efficiently in the multiple-inputs system, we may obtain more sophisticated functions than the single input systems. They will be fundamentals to develop multiple-inputs nonlinear systems, e.g., artificial neural networks, communications systems, and so on. Note that since the superposition theorem can not be applied to the nonlinear systems, the general analysis will be hard. Hence, we focus on a simple but important system and consider proper phenomena to the multiple-inputs case.