ﻻ يوجد ملخص باللغة العربية
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.
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks it is typic
We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop a
Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here we propose a new ansatz, based on the collective coord
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture the colle