eng Science and Education Publishing International Journal of Physics 2013-08-05 1 1 94 100 10.12691/ijp-1-4-3 IJP2013143 article Arindam Chakraborty 1 Anirban Ray 2 A. Roy Chowdhury asesh_r@yahoo.com 2 Department of Physics, Swami Vivekananda Institute of Science and Technology, Sonarpur, Kolkata, India High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata, India 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. http://pubs.sciepub.com/ijp/1/4/3/ijp-1-4-3.pdf discreet Kuramoto oscillators bifurcation Poincare section