Regular and irregular modulation of frequencies in limit cycle oscillator networks

ERATO Complex Systems Biology Project, JST - 3-8-1, Komaba, Meguro-ku, Tokyo 153-8902, Japan

^a mtach@riken.jp

Received: 29 December 2009
Accepted: 6 October 2010

Abstract

Nonisochronicity (frequency change caused by amplitude deviation) is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of nonisochronic limit cycle oscillators, and demonstrated that the frequencies assume distributed values in a sustainable manner. We observed two complex phenomena in the networks: stationary distributed frequencies at a regular interval (quantization of frequencies), and continuous irregular modulation of frequencies. In the analysis we reveal the mechanisms by which the frequencies are distributed, and show how the nonisochronicity produces these complex phenomena. We also illustrate that the topology of the networks determines the behavior of the system.