Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2008-12-19
J. Stat. Phys,136, (3), 565-602 (2009)
Nonlinear Sciences
Adaptation and Self-Organizing Systems
39 pages, 3 figures
Scientific paper
This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.
Cessac Bruno
Rostro H.
Vasquez Juan Carlos
Viéville Thierry
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