Science and Education Publishing International Journal of Physics 1 1 2013 08 05 Finite Kuramoto System with Shear and Symmetry 94 100 EN Arindam Chakraborty Anirban Ray A. Roy Chowdhury High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata, India IJP2013143 10.12691/ijp-1-4-3 2013 07 23 2013 08 02 2013 08 05 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.