Synchrony and Asynchrony in a Fully Stochastic Neural Network
We describe and analyze a model for a stochastic pulse-coupled neural network, in which the randomness in the model corresponds to synaptic failure and random external input. We show that the network can exhibit both synchronous and asynchronous behavior, and surprisingly, that there exists a range of parameters for which the network switches spontaneously between synchrony and asynchrony. We analyze the associated mean-field model and show that the switching parameter regime corresponds to a bistability in the mean field, and that the switches themselves correspond to rare events in the stochastic system.
KeywordsNeural network Neuronal network Synchronization Mean-field analysis Stochastic integrate-and-fire Bistability Rare events
Unable to display preview. Download preview PDF.
- Beggs, J.M., Plenz, D., 2003. Neuronal avalanches in neocortical circuits. J. Neurosci. 23(35), 11167–11177. Google Scholar
- Huygens, C., 1673. Horoloquium Oscilatorium. Parisiis, Paris. Google Scholar
- Peskin, C.S., 1975. Mathematical aspects of heart physiology. Courant Institute of Mathematical Sciences New York University, New York. Notes based on a course given at New York University during the year 1973/74, available at http://math.nyu.edu/faculty/peskin/heartnotes/index.html. zbMATHGoogle Scholar
- Pikovsky, A., Rosenblum, M., Kurths, J., 2003. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge. Google Scholar
- Strogatz, S., Sync: The Emerging Science of Spontaneous Order. Hyperion, 2003. Google Scholar
- van Vreeswijk, C., Abbott, L., Ermentrout, G., 1994. When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci. 313–322. Google Scholar