Finite Kuramoto System with Shear and Symmetry

Arindam Chakraborty¹, Anirban Ray² and A. Roy Chowdhury^2,

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

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

Cite this paper:
Arindam Chakraborty, Anirban Ray and A. Roy Chowdhury. Finite Kuramoto System with Shear and Symmetry. International Journal of Physics. 2013; 1(4):94-100. doi: 10.12691/ijp-1-4-3

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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