Delays and weakly coupled neuronal oscillators.
We use weakly coupled oscillator theory to study the effects of delays on coupled systems of neuronal oscillators. We explore, first, simple pairs with constant delays and then examine the role of distributed delays as would occur in systems with dendritic branches or in networks where there is a distance-dependent conductance delay. In the latter, we use mean field theory to show the emergence of travelling waves and the loss of synchronization. Next, we consider phase models with stronger coupling and delays in the state variables. We show that they have a richer dynamics but one that is still similar to the weakly coupled case.
Ermentrout
Bard
B
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. bard@pitt.edu
Ko
Tae-Wook
TW
D001519:Behavior; D002940:Circadian Rhythm; D003712:Dendrites / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009424:Nervous System Physiological Phenomena; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry; D010507:Periodicity; D011930:Reaction Time / Q000502:physiology*