One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 6, 2012, Pages

  Gupta, Shamik ^a   Potters, Max ^a,b   Ruffo, Stefano ^a,c  

^a UNIVERSITÉ DE LYON   (France)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUITY EQUATIONS; CONTINUUM LIMITS; FOURIER MODES; IN-PHASE; LATTICE LENGTH; LOCAL DENSITY; ONE-DIMENSIONAL LATTICE; OSCILLATOR FREQUENCY; PERIODIC LATTICES; POWER-LAW; STABILITY THRESHOLDS; STATIONARY SOLUTIONS;

COMPUTER SIMULATION; DYNAMICS; LINEAR STABILITY ANALYSIS;

FOURIER TRANSFORMS;

EID: 84862156782     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.066201     Document Type: Article

References (22)

1. A. K. Ghosh, B. Chance, and E. K. Pye, Arch. Biochem. Biophys. ABBIA4 0003-9861 10.1016/0003-9861(71)90042-7 145, 319 (1971).
2. J. Aldridge and E. K. Pye, Nature (London) NATUAS 0028-0836 10.1038/259670a0 259, 670 (1976).
3. C. S. Peskin, Mathematical Aspects of Heart Physiology (Courant Institute of Mathematical Science Publication, New York, 1975).
4. D. C. Michaels, E. P. Matyas, and J. Jalife, Circulation Res. 61, 704 (1987).
5. J. Buck and E. Buck, Sci. Am. SCAMAC 0036-8733 10.1038/ scientificamerican0576-74 234, 74 (1976).
6. J. Buck, Quart. Rev. Biol. QRBIAK 0033-5770 10.1086/415929 63, 265 (1988).
7. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.404 76, 404 (1996).
8. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. E 1539-3755 10.1103/PhysRevE.57.1563 57, 1563 (1998).
9. A. Pikovsky, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2003).
10. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984).
11. S. H. Strogatz, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(00)00094-4 143, 1 (2000).
12. J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77. 137 77, 137 (2005). (Pubitemid 41490657)
13. P. König, A. K. Engel, and W. Singer, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.92.1.290 92, 290 (1995).
14. J. L. Rogers and L. T. Wille, Phys. Rev. E 1539-3755 10.1103/PhysRevE.54. R2193 54, R2193 (1996).
15. M. S. O. Massunaga and M. Bahiana, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02)00501-8 168, 136 (2002). (Pubitemid 34802472)
16. A. Pikovsky and M. Rosenblum, Physica D PDNPDT 0167-2789 10.1016/j.physd.2011.01.002 240, 872 (2011).
17. D. Chowdhury and M. C. Cross, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.016205 82, 016205 (2010).
18. M. Maródi, F. d'Ovidio, and T. Vicsek, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.011109 66, 011109 (2002). (Pubitemid 40598960)
19. R. Bachelard, T. Dauxois, G. De Ninno, S. Ruffo, and F. Staniscia, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.061132 83, 061132 (2011).
20. A. Campa (private communication).
21. R. E. Mirollo and S. H. Strogatz, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01013676 60, 245 (1990).
22. H. M. Antia, Numerical Methods for Scientists and Engineers, 2nd ed. (Birkhauser, Basel, 2002).