Excitatory and inhibitory interactions in populations of model neurons (Wilson and Cowan 1972)

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Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.
1 . Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12:1-24 [PubMed]
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Model Type: Realistic Network;
Brain Region(s)/Organism: Generic;
Cell Type(s):
Gap Junctions:
Simulation Environment: NEURON; XPPAUT;
Model Concept(s): Activity Patterns;
Implementer(s): Lytton, William [bill.lytton at downstate.edu]; Ermentrout, Bard [bard_at_pitt.edu];
From Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons
Hugh R. Wilson and Jack D. Cowan; Biophys J. 1972 January; 12:1-24.

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This implementation was copied from Bard Ermentrout's xppaut file: wc.ode