Analyzing Stable Solutions of 3×3 and 3×4 van der Pol Oscillators Coupled as a Torus Shape

Abstract

Synchronization phenomena are observed in many situations and places, and are used for various purposes. Many synchronization phenomena in coupled van der Pol oscillators, which are electronic circuits, have been analyzed and reported. We previously discovered and reported a wavelike propagating phase state between adjacent oscillators. However, the analysis of many synchronization phenomena is not yet sufficient and is a very important task. In this paper, we analyze synchronization states on torus shapes in which the number of oscillators per column is three and the number of oscillators per row is three or four. Furthermore, theoretical results are compared with simulation results.