Open Access Peer-reviewed

Finite Kuramoto System with Shear and Symmetry

Arindam Chakraborty1, Anirban Ray2, A. Roy Chowdhury2,

1Department of Physics, Swami Vivekananda Institute of Science and Technology, Sonarpur, Kolkata, India

2High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata, India

International Journal of Physics. 2013, 1(4), 94-100. DOI: 10.12691/ijp-1-4-3
Published online: August 25, 2017

Abstract

In this paper we study the locally coupled finite Kuramoto Oscillator system with shear under periodic boundary condition. We also show how analytical solutions can be obtained from symmetry conditions. Existence of attractors and bifurcation patterns are revealed in an elegant way through these solutions. The synchronized regions are identified in the parameter space and critical situations are discussed. an important outcome of present analysis is the derivation of analytical form of the Poincare map.

Keywords:

discreet Kuramoto oscillators, bifurcation, Poincare section
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