NDLI: Synchronized Activity and Loss of Synchrony Among Heterogeneous Conditional Oscillators

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Synchronized Activity and Loss of Synchrony Among Heterogeneous Conditional Oscillators

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rubin, Jonathan Terman, David
Copyright Year	2002
Abstract	The inspiratory phase of the respiratory rhythm involves the synchronized bursting of a network of neurons in the brain stem. This paper considers activity patterns in a reduced model for this network, namely, a system of conductance-based ordinary differential equations with excitatory synaptic coupling, incorporating heterogeneities across cells. The model cells are relaxation oscillators; that is, no spikes are included. In the continuum limit, under assumptions based on the disparate time scales in the model, we derive consistency conditions sufficient to give tightly synchronized oscillations; when these hold, we solve a fixed point equation to find a unique synchronized periodic solution. This solution is stable within a certain solution class, and we provide a general sufficient condition for its stability. Allowing oscillations that are less cohesive but still synchronized, we derive an ordinary differential equation boundary value problem that we solve numerically to find a corresponding periodic solution. These results help explain how heterogeneities among synaptically coupled oscillators can enhance the tendency toward synchronization of their activity. Finally, we consider conditions for synchrony to break down.
Starting Page	146
Ending Page	174
Page Count	29
File Format	PDF
DOI	10.1137/S111111110240323X
e-ISSN	15360040
Issue Number	1
Volume Number	1
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-07
Access Restriction	Subscribed
Subject Keyword	Relaxation oscillations Integro-ordinary differential equations Nonlinear oscillations, coupled oscillators synaptic coupling Fixed points, periodic points, fixed-point index theory oscillations synchrony heterogeneity respiratory rhythm Neural biology
Content Type	Text
Resource Type	Article

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