Delays and weakly coupled neuronal oscillators.

作者: Bard Ermentrout , Tae-Wook Ko

DOI: 10.1098/RSTA.2008.0259

关键词: Coupling (physics)Mean field theorySynchronizationConductancePhase (waves)MathematicsStatistical physicsTraveling waveControl theoryState variableConstant (mathematics)

摘要: We use weakly coupled oscillator theory to study the effects of delays on systems neuronal oscillators. explore, first, simple pairs with constant and then examine role distributed as would occur in dendritic branches or networks where there is a distance-dependent conductance delay. In latter, we mean field show emergence travelling waves loss synchronization. Next, consider phase models stronger coupling state variables. that they have richer dynamics but one still similar case.

参考文章(35)
Michael C. Mackey, Leon Glass, From clocks to chaos ,(1988)
Rafael Yuste, Jason N. MacLean, Jeffrey Smith, Anders Lansner, The cortex as a central pattern generator Nature Reviews Neuroscience. ,vol. 6, pp. 477- 483 ,(2005) , 10.1038/NRN1686
S.M. Crook, G.B. Ermentrout, M.C. Vanier, J.M. Bower, The role of axonal delay in the synchronization of networks of coupled cortical oscillators. Journal of Computational Neuroscience. ,vol. 4, pp. 161- 172 ,(1997) , 10.1023/A:1008843412952
Sharon M. Crook, G. Bard Ermentrout, James M. Bower, Dendritic and synaptic effects in systems of coupled cortical oscillators. Journal of Computational Neuroscience. ,vol. 5, pp. 315- 329 ,(1998) , 10.1023/A:1008839112707
Eugene M. Izhikevich, Dynamical Systems in Neuroscience ,(2006)
E.H Buhl, M.A Whittington, R.D Traub, N Kopell, B Ermentrout, Inhibition-based rhythms: experimental and mathematical observations on network dynamics International Journal of Psychophysiology. ,vol. 38, pp. 315- 336 ,(2000) , 10.1016/S0167-8760(00)00173-2
George Bard Ermentrout, Nancy Kopell, Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. SIAM Journal on Mathematical Analysis. ,vol. 15, pp. 215- 237 ,(1984) , 10.1137/0515019
Y. Nakamura, F. Tominaga, T. Munakata, Clustering behavior of time-delayed nearest-neighbor coupled oscillators Physical Review E. ,vol. 49, pp. 4849- 4856 ,(1994) , 10.1103/PHYSREVE.49.4849
Seong-Ok Jeong, Tae-Wook Ko, Hie-Tae Moon, Time-delayed spatial patterns in a two-dimensional array of coupled oscillators. Physical Review Letters. ,vol. 89, pp. 154104- ,(2002) , 10.1103/PHYSREVLETT.89.154104
H. G. Schuster, P. Wagner, Mutual Entrainment of Two Limit Cycle Oscillators with Time Delayed Coupling Progress of Theoretical Physics. ,vol. 81, pp. 939- 945 ,(1989) , 10.1143/PTP.81.939