Hiroyuki Torikai | PubMed Health

PubMed2004

Synchronization phenomena in pulse-coupled networks driven by spike-train inputs.

We present a pulse-coupled network (PCN) of spiking oscillators (SOCs) which can be implemented as a simple electrical circuit. The SOC has a periodic reset level that can realize rich dynamics represented by chaotic spike-trains. Applying a spike-train input, the PCN can exhibit the following interesting phenomena. 1) Each SOC synchronizes with a part of the input without overlapping, i.e., the input is decomposed. 2) Some SOCs synchronize with a part of the input with overlapping, i.e., the input is decomposed and the SOCs are clustered. The PCN has multiple synchronization phenomena and exhibits one of them depending on the initial state. We clarify the numbers of the synchronization phenomena and the parameter regions in which these phenomena can be observed. Also stability of the synchronization phenomena is clarified. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

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Rich dynamics of pulse-coupled spiking neurons with a triangular base signal.

This paper presents a spiking neuron circuit with a triangular base signal. The circuit can output rich pulse-trains and the dynamics can be analyzed using a piecewise linear one-dimensional pulse-position map. Applying cross-switching to two neurons we construct a pulse-coupled system whose dynamics can be integrated into a composite map of the pulse position maps of two neurons. The composite map is piecewise linear and precise analysis is possible. We can clarify various interesting phenomena caused by the pulse-coupling. For example, periodic behavior of each neuron is changed into chaotic behavior and chaotic behavior of each neuron is changed into periodic behavior. These results provide basic information to construct flexible pulse-coupled neural networks.

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