TY - JOUR
T1 - Dynamics of two mutually coupled slow inhibitory neurons
AU - Terman, D.
AU - Kopell, N.
AU - Bose, A.
N1 - Funding Information:
Synchronous activity in networks of inhibitory neurons has been observed in thalamic \[23\]a nd hippocampal \[34\] networks. Such an activity has been the subject of a large number of simulation studies \[1,3,7-9,11,16,26,28-31,33\]. For coupled neural oscillators, a traditional view is that excitatory coupling leads to synchronous behavior, while inhibitory coupling leads to asynchronous behavior. Though this has been supported by many modeling studies \[5,12,19-21\],t here has recently been a variety of studies whose conclusion is the opposite \[4,5,28,30,31\]. Several of these papers emphasize the importance to the network behavior of the rates at which the synapses activate or * Corresponding author. E-mail: [email protected]. Supported in part by NSF ~:ant DMS-9423796. 1 E-maih [email protected]. Supported in part by NSF grant DMS-9200131 and NIMH grant MH47510. 2 E-mail: bose @n imbu.njit.edu.
PY - 1998
Y1 - 1998
N2 - Inhibition in oscillatory networks of neurons can have apparently paradoxical effects, sometimes creating dispersion of phases, sometimes fostering synchrony in the network. We analyze a pair of biophysically modeled neurons and show how the rates of onset and decay of inhibition interact with the timescales of the intrinsic oscillators to determine when stable synchrony is possible. We show that there are two different regimes in parameter space in which different combinations of the time constants and other parameters regulate whether the synchronous state is stable. We also discuss the construction and stability of nonsynchronous solutions, and the implications of the analysis for larger networks. The analysis uses geometric techniques of singular perturbation theory that allow one to combine estimates from slow flows and fast jumps.
AB - Inhibition in oscillatory networks of neurons can have apparently paradoxical effects, sometimes creating dispersion of phases, sometimes fostering synchrony in the network. We analyze a pair of biophysically modeled neurons and show how the rates of onset and decay of inhibition interact with the timescales of the intrinsic oscillators to determine when stable synchrony is possible. We show that there are two different regimes in parameter space in which different combinations of the time constants and other parameters regulate whether the synchronous state is stable. We also discuss the construction and stability of nonsynchronous solutions, and the implications of the analysis for larger networks. The analysis uses geometric techniques of singular perturbation theory that allow one to combine estimates from slow flows and fast jumps.
KW - Inhibition
KW - Oscillations
KW - Synchronization
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U2 - 10.1016/S0167-2789(97)00312-6
DO - 10.1016/S0167-2789(97)00312-6
M3 - Article
AN - SCOPUS:0000821114
SN - 0167-2789
VL - 117
SP - 241
EP - 275
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -