Winding-number excitation in one-dimensional oscillators with variable interaction range

• Published in: Journal of the Korean Physical Society Vol. 64; no. 7; pp. 954 - 957
• Main Authors: Hong, Hyunsuk, Kim, Beom Jun
• Format: Journal Article
• Language: English
• Published: Seoul The Korean Physical Society 01.04.2014; 한국물리학회
• Subjects: Mathematical and Computational Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Theoretical; 물리학; Coupled oscillators; Interaction range; Twisted state; Winding number
• ISSN: 0374-4884; 1976-8524
• DOI: 10.3938/jkps.64.954

At how long of an interaction range does an oscillator system behave as a fully-connected one? To answer this question, we consider a system of nonlocally-coupled phase oscillators in one dimension, and explore the effects of a variable interaction range L on collective dynamics. In particular, we investigate the winding-number distribution, paying particular attention to the existence of a twisted wave in the system, and observe that the twisted state vanishes when the interaction range exceeds a critical value. Finite-size scaling of the width of the winding-number distribution reveals that the transition occurs at 2 L/N ≈ 0.6, regardless of the system size N . We also show that at the same transition point for the topological twisted state, the phase synchrony in the system becomes partial.