Synchronized activity and loss of synchrony amorsg heterogeneous conditional oscillators

SIAM Journal on Applied Dynamical Systems

Volumn 1, Issue 1, 2002, Pages 146-174

  Rubin, Jonathan ^a,b   Terman, David ^a,b  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Heterogeneity; Oscillations; Respiratory rhythm; Synaptic coupling; Synchrony

Indexed keywords

EID: 3042676195     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/S111111110240323X     Document Type: Article

References (22)

1. J. T. Ariaratnam and S. H. Strogatz, Phase diagram for the Winfree model of coupled nonlinear oscillators, Phys. Rev. Lett., 86 (2001), pp. 4278-4281.
2. R. Butera, J. Rinzel, and J. Smith, Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons, J. Neurophysiology, 81 (1999), pp. 382-397.
3. R. Butera, J. Rinzel, and J. Smith, Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations of coupled pacemaker neurons, J. Neurophysiology, 81 (1999), pp. 398-415 .
4. C. C. Chow, Phaselocking in weakly heterogeneous neuronal networks, Phys. D, 118 (1998), pp. 343-370.
5. G. de Vries and A. Sherman, From spikers to bursters via coupling: Help from heterogeneity, Bull. Math. Biol., 63 (2002), pp. 371-391.
6. C. DelNegro, S. Johnson, R. Butera, and J. Smith, Models of respiratory rhythm generation in the pre-Bötzinger complex. III. Experimental tests of model predictions, J. Neurophysiology, 86 (2001), pp. 59-74.
7. C. DelNegro, C. Wilson, R. Butera, H. Rigatto, and J. Smith, Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network, Biophys. J., 82 (2002), pp. 206-214.
8. G. B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, Software Environ. Tools 14, SIAM, Philadelphia, 2002.
9. G. B. Ermentrout and N. Kopell, Frequency plateaus in a chain of weakly coupled oscillators, SIAM J. Math. Anal., 15 (1984), pp. 215-237.
10. D. Golomb and J. Rinzel, Dynamics of globally coupled inhibitory neurons with heterogeneity, Phys. Rev. E (3), 48 (1993), pp. 4810-4814.
11. D. Golomb, X.-J.Wang, and J. Rinzel, Synchronization properties of spindle oscillations in a thalamic reticular nucleus model, J. Neurophysiology, 72 (1994), pp. 1109-1126.
12. S. Johnson, J. Smith, G. Funk, and J. Feldman, Pacemaker behavior of respiratory neurons in medullary slices from neonatal rat, J. Neurophysiology, 72 (1994), pp. 2598-2608.
13. N. Kopell and G. B. Ermentrout, Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators, in Handbook of Dynamical Systems, Vol. 2: Towards Applications, B. Fiedler ed., North-Holland, Amsterdam, 2002, pp. 3-54.
14. N. Koshiya and J. Smith, Neuronal pacemaker for breathing visualized in vitro, Nature, 400 (1999), pp. 360-363.
15. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, Berlin, 1984.
16. J. Rubin and D. Terman, Geometric singular perturbation analysis of neuronal dynamics, in Handbook of Dynamical Systems, Vol. 2: Towards Applications, B. Fiedler ed., North-Holland, Amsterdam, 2002, pp. 93-146.
17. J. Smith, H. Ellengerger, K. Ballanyi, D. Richter, and J. Feldman, Pre-Bötzinger complex: A brainstem region that may generate respiratory rhythm in mammals, Science, 254 (1991), pp. 726-729.
18. D. Somers and N. Kopell, Rapid synchronization through fast threshold modulation, Biol. Cybern., 68 (1993), pp. 393-407.
19. D. Somers and N. Kopell, Waves and synchrony in networks of oscillators of relaxation and nonrelaxation type, Phys. D, 89 (1995), pp. 169-183.
20. D. Terman and D. L. Wang, Global competition and local cooperation in a network of neural oscillators, Phys. D, 81 (1995), pp. 148-176.
21. J. White, C. C. Chow, J. Ritt, C. Soto, and N. Kopell, Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons, J. Comput. Neurosci., 5 (1998), pp. 5-16.
22. A. Winfree, Biological rhythms and the behavior of coupled oscillators, J. Theoret. Biol., 16 (1967), pp. 15-42.