Synchronization in networks of limit cycle oscillators

Zeitschrift fur Physik B-Condensed Matter

Volumn 100, Issue 2, 1996, Pages 303-320

  Tass, Peter ^a,b   Haken, Hermann ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

^b HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003333284     PISSN: 07223277     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002570050126     Document Type: Article

References (24)

1. Aizawa, Y.: Synergetic approach to the phenomena of mode-locking in nonlinear systems. Prog. Theor. Phys. 56, 703-716 (1976)
2. Christiansen, B., Alstrom, P., Levinsen, M.T.: Collective dynamics of coupled modulated oscillators with random pinning. Physica D 56, 23-35 (1992)
3. Cohen, A.H., Holmes, P.J., Rand, R.H.: The nature of coupling between sequential oscillators and the lamprey spinal generator for locomotion: a mathematical model. J. Math. Biol. 13, 345-369 (1982)
4. Eckhorn, R., Bauer, R., Jordan, W., Brosch, M., Kruse, W., Munk, M., Reitboeck, H.J.: Coherent Oscillations: A Mechanism of feature linking in the visual cortex? Biol. Cybern. 60, 121-130 (1988)
5. Elphick, C., Tirapegui, E., Brachet, M., Coullet, P., Iooss, G.: A simple global characterization for normal forms of singular vector fields. Physica D 29, 95-127 (1987)
6. Ermentrout, G.B.: Synchronization in a pool of mutually coupled oscillators with random frequencies. J. Math. Biology 22, 1-9 (1985)
7. Ermentrout, G.B., Kopell, N.: Frequency plateaus in a chain of weakly coupled oscillators. I. SIAM J. Math. Anal. 15, 215-237 (1984)
8. Gray, C.W., Singer, W.: Stimulus specific neuronal oscillations in the cat visual cortex: a cortical function unit. Soc. Neurosci 404, 3 (1987)
9. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Berlin, Heidelberg: Springer 1990
10. Haken, H.: Synergetics. An Introduction. Berlin, Heidelberg: Springer 1977
11. Haken, H.: Advanced Synergetics. Berlin, Heidelberg: Springer 1987
12. Haken, H., Kelso, J.A.S., Bunz, H.: A Theoretical Model of Phase Transitions in Human Hand Movements. Biol. Cybern. 51, 347-356 (1985)
13. Hale, J.K.: Ordinary Differential Equations. New York: Wiley (1969)
14. Ioos, G., Adelmeyer, M.: Topics in Bifurcation Theory and Applications. World Scientific, Advanced series in Nonlinear Dynamics, Vol.3, Singapore (1992)
15. Kelley, A.: The stable, center-stable, center, center-unstable and unstable manifolds. J. Diff. Equ. 3, 546-570 (1967)
16. Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Berlin, Heidelberg: Springer 1984
17. Murray, J.D.: Mathematical Biology. Berlin, Heidelberg: Springer 1989
18. Pliss, V.: Principal reduction in the theory of stability of motion. Izv. Akad. Nauk. SSSR Math. Ser. 28, 1297-1324 (1964)
19. Ruelle, D.: Bifurcations in the Presence of a Symmetry Group. Arch. Rat. Mech. Anal. 51, 136-152 (1973)
20. Stoer, J., Bulirsch, R.: Numerische Mathematik II. Berlin, Heidelberg: Springer 1990
21. Strogatz, S.H., Mirollo, R.E., Matthews, P.C.: Coupled Nonlinear Oscillators below the Synchronization Threshold: Relaxation by Generalized Landau Damping. Phys. Rev. Letters, vol. 68, No. 18, 2730-2733 (1992)
22. Struwe, M.: Variational Methods. Berlin, Heidelberg: Springer 1990
23. Tass, P.: Synchronisierte Oszillationen im visuellen Cortex - ein synergetisches Modell. Ph.D. thesis, University of Stuttgart (1993)
24. Tsodyks, M., Mitkov, I., Sompolinsky, H.: Pattern of Synchrony in Inhomogeneous Networks of Oscillators with Pulse Interactions. Phys. Rev. Lett. 71, (8), 1280-1283 (1993)