Similar nonleaky integrate-and-fire neurons with instantaneous couplings always synchronize

SIAM Journal on Applied Mathematics

Volumn 61, Issue 4, 2000, Pages 1143-1155

  Senn, Walter ^a   Urbanczik, Robert ^a,b  

^a UNIVERSITY OF BERN   (Switzerland)

^b UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

Integrate and fire; Pacemaker; Pulse coupled biological oscillators; Synchronization

Indexed keywords

FREQUENCY RESPONSE; FUNCTIONS; GLOBAL OPTIMIZATION; INITIAL VALUE PROBLEMS; LINEAR SYSTEMS; MATHEMATICAL MODELS; SYNCHRONIZATION; THEOREM PROVING;

GLOBAL SYNCHRONIZATION; INSTANTANEOUS COUPLINGS; NONLEAKY INTEGRATE-AND-FIRE NEURONS; PESKIN MODEL; PULSE-COUPLED NEURONS;

PULSE GENERATORS;

EID: 0034844437     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036139998346038     Document Type: Article

References (32)

1. L. F. ABBOTT, A network of oscillators, J. Phys. A, 23 (1990), pp. 3835-3859.
2. L. F. ABBOTT AND C. VAN VREESWIJK, Asynchronous states in networks of pulse-coupled oscillators, Phys. Rev. E (3), 48 (1993), pp. 1483-1490.
3. S. BOTTANI, Pulse-coupled relaxation oscillators: From biological synchronization to self-organized criticality, Phys. Rev. Lett., 74 (21) (1995), pp. 4189-4192.
4. A. BRAILOVE, The dynamics of two pulse-coupled relaxation oscillators, Int. J. of Bifurcation and Chaos, 2 (1992), pp. 341-352.
5. P. BRESSLOFF AND S. COOMBES, Desynchronization, Mode Locking, and Bursting in Strongly Coupled Integrate-and-Fire Oscillators, Phys. Rev. Lett., 81 (1998), pp. 2168-2171.
6. P. BRESSLOFF AND S. COOMBES, Spike train dynamics underlying pattern formation in integrate-and-fire oscillator networks, Phys. Rev. Lett., 81 (1998), pp. 2384-2387.
7. J. BUCK, Synchronous rhythmic flashing of fireflies. II, Quart. Rev. Biol., 63 (1988), pp. 265-289.
8. C. CHOW, Phase-locking in weakly heterogeneous neuronal networks, Phys. D, 118 (1998), pp. 343-370.
9. E. DOMANY, J. L. VAN HEMMEN, AND K. SCHULTEN, EDS., Models of Neural Networks II, Temporal Aspects of Coding and Information Processing in Biological Systems, Springer-Verlag, Berlin, 1994.
10. A. K. ENGEL, P. KÖNIG, A. K. KREITER, T. B. SCHILLEN, AND W. SINGER, Temporal coding in the visual cortex: New vistas on integration in the nervous system, Trends in Neurosci., (1992), pp. 218-226.
11. J. T. ENRIGHT, Temporal precision in circadian systems: A reliable neuronal clock from unreliable components?, Science, 209 (1980), pp. 1542-1545.
12. U. ERNST, K. PAWELZIK, AND T. GEISEL, Delay-induced multistage synchronization of biological oscillators, Phys. Rev. E (3), 57 (1998), pp. 2150-2162.
13. W. GERSTNER, Rapid phase locking in systems of pulse-coupled oscillators with delays, Phys. Rev. Lett., 76 (1996), pp. 1755-1758.
14. W. GERSTNER, J. L. VAN HEMMEN, AND J. D. COWAN, What matters in neuronal locking, Neural Computation, 8 (1996), pp. 1653-1676.
15. D. GOLOMB AND J. RINZEL, Dynamics of globally coupled inhibitory neurons with heterogeneity, Phys. Rev. E (3), 60 (1999), pp. 4810-1811.
16. P. HADLEY, M. BEASLY, AND K. WIESENFELD, Phase-locking of Josephson-junction series arrays, Phys. Rev. B, 38 (1988), pp. 8712-8719.
17. D. HANSEL, G. MATO, AND C. MEUNIER, Synchrony in excitatory neural networks, Neural Computation, 7 (1995), pp. 307-337.
18. A. V. M. HERZ AND J. J. HOPFIELD, Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements, Phys. Rev. Lett., 75 (1995), pp. 1222-1225.
19. Y. KURAMOTO, Chemical Oscillations, Waves and Turbulence, Springer-Verlag, New York, 1984.
20. Y. KURAMOTO, Collective synchronization of pulse-coupled oscillators and excitable units, Phys. D, 50 (1991), pp. 15-30.
21. K. MACLEOD AND G. LAURENT, Distinct mechanisms for synchronization and temporal patterning of odor-encoding neural assemblies, Science, 274 (1996), pp. 976-979.
22. R. E. MIROLLO AND S. H. STROGATZ, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), pp. 1645-1662.
23. Z. OLAMI, Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes, Phys. Rev. Lett., 68 (1992), pp. 1244-1247.
24. C. PÉREZ, A. CORRAL, A. DÍAZ-GUILERA, AND K. C. AND A. ARENAS, On self-organized criticality and synchronization in lattice models of coupled dynamical systems, Int. J. of Modern Physics B, 10 (1996), pp. 1111-1151.
25. C. S. PESKIN, Mathematical Aspects of Heart Physiology, Courant Institute of Mathematical Science, New York University, New York, 1975.
26. S. H. STROGATZ AND I. STEWART, Coupled oscillators and biological synchronization, Scientific American, 269 (1993), pp. 102-109.
27. D. TERMAN, N. KOPELL, AND A. BOSE, Dynamics of two mutually inhibitory neurons, Phys. D, 117 (1998), pp. 241-275.
28. R. D. TRAUB, R. MILES, AND R. K. S. WONG, Model of the origin of rhythmic population Oscillations in the hippocampal slice, Science, 243 (1989), pp. 1319-1325.
29. M. TSODYKS, I. MITKOV, AND H. SOMPOLINSKY, Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions, Phys. Rev. Lett., 71 (1993), pp. 1280-1283.
30. C. VAN VREESWIJK, L. ABBOTT, AND G. ERMENTROUT, When inhibition not excitation synchronizes neural firing., J. Comp. Neurosci, 1 (1994), pp. 313-322.
31. A. T. WINFREE, The Geometry of Biological Time, Springer-Verlag, New York, 1980.
32. H. WINFUL AND S. WANG, Stability of phase locking in coupled semiconductor laser arrays, Appl. Phys. Lett., 53 (1988), pp. 1894-1896.