Phase resetting and coupling of noisy neural oscillators

Journal of Computational Neuroscience

Volumn 20, Issue 2, 2006, Pages 179-190

  Ermentrout, Bard ^a   Saunders, David ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Neural oscillators; Noise; Phase resetting; Pulsatile coupling

Indexed keywords

INTELLIGENT SYSTEMS; STOCHASTIC SYSTEMS;

EXPERIMENTAL GROUPS; INVARIANT DENSITIES; NEURAL OSCILLATOR; NOISE; PHASE COUPLING; PHASE RESETTING; PHASE RESPONSE CURVES; PULSATILE COUPLING; PULSATILES; STOCHASTICS;

MONTE CARLO METHODS;

ARTICLE; BRAIN NERVE CELL; COMPUTER ANALYSIS; CONTROLLED STUDY; MONTE CARLO METHOD; NOISE; NONLINEAR SYSTEM; OSCILLATION; PRIORITY JOURNAL; SIMULATION; STATISTICAL ANALYSIS;

EID: 33646522150     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-005-5427-0     Document Type: Article

References (22)

1. Acebron JA, Bonilla LL, Prez Vicente, CJ, Ritort F, Spigler R (2005) The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of Modern Physics 77: 137-185.
2. Ariaratnam JT, Strogatz SH (2001) Phase diagram for the Winfree model of coupled nonlinear oscillators. Phys. Rev. Lett. 86: 4278-4281.
3. Buzsaki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304: 1926-1929.
4. Chow CC, White JA, Ritt, J, Kopell N (1998) Frequency control in synchronized networks of inhibitory neurons. J. Comput. Neurosci. 5: 407-420.
5. Ermentrout B, Pascal M, Gutkin B (2001) The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Computation 13: 1285-1310.
6. Galan RF, Ermentrout GB, Urban NN (2005) Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. Phys. Rev. Lett. 94: 158101.
7. Gardiner CW (1997) Handbook of Stochastic Methods (2nd edition). Springer, New York.
8. Goel P, Ermentrout B (2002) Synchrony, stability, and firing patterns in pulse-coupled oscillators Physica D 163: 191-216.
9. Izhikevich EM (2003) Simple model of spiking neurons. IEEE Transactions on Neural Networks 14: 1569-1572.
10. Jones SR, Pinto DJ, Kaper TJ, Kopell N (2000) Alpha-frequency rhythms desynchronize over long cortical distances: A modeling study. J. Comput. Neurosci. 9: 271-91.
11. Lasota A, Mackey MC (1986) Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer Applied Mathematical Science 97. Springer-Verlag, Berlin (Chapt. 10.5).
12. Lindner B, Garcia-Ojalvo J, Neiman A, Schimansky-Geier L (2004) Effects of noise in excitable systems, Phys. Rep. 392, 321.
13. Mirollo RM, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. SIAM. J. Appl. Math. 50: 1645-1662.
14. Netoff TI, Banks MI, Dorval AD, Acker CD, Haas JS, Kopell N, White JA (2005) Synchronization in hybrid neuronal networks of the hippocampal formation. J. Neurophysiol. 93: 1197-208.
15. Oprisan SA, Canavier CC (2000) Phase response curve via multiple time scale analysis of limit cycle behavior of type I and type II excitability. Biophys. J. 78: 218-230.
16. Reyes AD, Fetz EE (1993) Effects of transient depolarizing potentials on the firing rate of cat neocortical neurons. J. Neurophysiol. 69: 1673-183.
17. Rodriguez R, Tuckwell HC (1996) Statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks. Physical Review E 54: 5585-5590.
18. Sompolinsky H, Golomb D, Kleinfeld D (1991) Phase coherence and computation in a neural network of coupled oscillators. In: Non-Linear Dynamics and Neural Networks, H.G. Schuster and W Singer Eds. (VCH, Weinheim, 1991), pp. 113-140.
19. Stoop R, Schindler K, Bunimovich LA (2000) Neocortical networks of pyramidal neurons: From local locking and chaos to macroscopic chaos and synchronization. Nonlinearity 13: 1515-1529.
20. Strogatz, S (2000) From Kuramoto to Crawford: Explaining the onset of synchronization in populations of globally coupled oscillators. Physica D 143: 1-20.
21. Tass PA (2003) Stochastic phase resetting of two coupled phase oscillators stimulated at different times. Phys. Rev. E 67:05 1902.
22. Van Vreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci. 1: 313-321.