- Access by Xinjiang University
Synchronization in an ensemble of spatially moving oscillators with linear and nonlinear coupling schemes
Phys. Rev. E 86, 056213 – Published 26 November, 2012
DOI: https://doi.org/10.1103/PhysRevE.86.056213
Abstract
We study synchronization in an ensemble of oscillators residing in a finite two-dimensional space. The interaction between the oscillators is governed by their spatial movement. The coupling is unidirectional and is of the intermediate kind, with the spatial vision of each oscillator deciding the number of oscillators to which it is coupled. We also analyze how the extent of synchronization, characterized by the order parameter, depends upon the system parameters, such as spatial vision, spatial motion, and strength of the coupling. The model systems employed here are the Van der Pol oscillator and the Brusselator. Furthermore, for the same spatial configuration, both linear and nonlinear coupling schemes are studied and their results compared.
Article Text
References (20)
- S. Strogatz, The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
- S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) (Perseus Books, Cambridge, MA, 2001).
- K. S. Thornburg, Jr., M. Möller, R. Roy, T. W. Carr, R. D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
- P. Ashwin, J. R. Terry, K. S. Thornburg, Jr., and R. Roy, Phys. Rev. E 58, 7186 (1998).
- I. Z. Kiss, J. L. Hudson, J. Escalona, and P. Parmananda, Phys. Rev. E 70, 026210 (2004).
- C. Masoller, H. L. D. de S. Cavalcante, and J. R. Rios Leite, Phys. Rev. E 64, 037202 (2001).
- I. Z. Kiss, V. Gaspard, and J. L. Hudson, J. Phys. Chem. B 104, 7554 (2000).
- L. Glass, Nature (London) 410, 277 (2001).
- M. Frasca, A. Buscarino, A. Rizzo, L. Fortuna, and S. Boccaletti, Phys. Rev. Lett. 100, 044102 (2008).
- M. A. Harrison, Y.-Ch. Lai, and R. D. Holt, Phys. Rev. E 63, 051905 (2001).
- R. Mirollo and S. Strogatz, SIAM J. Appl. Math. 50, 1645 (1990).
- I. T. Tokuda, S. Jain, I. Z. Kiss, and J. L. Hudson, Phys. Rev. Lett. 99, 064101 (2007).
- G. Schmidt, Phys. Lett. A 243, 205 (1998).
- S. Bottani, Phys. Rev. Lett. 74, 4189 (1995).
- G. B. Ermentrout, J. Math. Biol. 29, 571 (1991).
- G. B. Ermentrout and J. Rinzel, Am. J. Physiol. 246, R102 (1984).
- T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).
- A. Garcia Cantu Ros, Ch. G. Antonopoulos, and V. Basios, Chaos Solitons Fractals 44, 574 (2011).
- J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995).
- S. Sarkar and P. Parmananda, Chaos 20, 043108 (2010).