From Neuron to Neural Networks dynamics

09/15/2006
by   B. Cessac, et al.
0

This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the Hodgkin-Huxley description, which is somehow the canonical description for the "biological neuron". We discuss some models reducing the Hodgkin-Huxley model to a two dimensional dynamical system, keeping one of the main feature of the neuron: its excitability. We present then examples of phase diagram and bifurcation analysis for the Hodgin-Huxley equations. Finally, we end this section by a dynamical system analysis for the nervous flux propagation along the axon. We then consider neuron couplings, with a brief description of synapses, synaptic plasticiy and learning, in a second section. We also briefly discuss the delicate issue of causal action from one neuron to another when complex feedback effects and non linear dynamics are involved. The third section presents the limit of weak coupling and the use of normal forms technics to handle this situation. We consider then several examples of recurrent models with different type of synaptic interactions (symmetric, cooperative, random). We introduce various techniques coming from statistical physics and dynamical systems theory. A last section is devoted to a detailed example of recurrent model where we go in deep in the analysis of the dynamics and discuss the effect of learning on the neuron dynamics. We also present recent methods allowing the analysis of the non linear effects of the neural dynamics on signal propagation and causal action. An appendix, presenting the main notions of dynamical systems theory useful for the comprehension of the chapter, has been added for the convenience of the reader.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/13/2022

Physics guided neural networks for modelling of non-linear dynamics

The success of the current wave of artificial intelligence can be partly...
research
08/24/2022

Spectrum of non-Hermitian deep-Hebbian neural networks

Neural networks with recurrent asymmetric couplings are important to und...
research
04/26/2023

Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models

We introduce a new approach for solving forward systems of differential ...
research
11/19/2020

Deep Learning with a Single Neuron: Folding a Deep Neural Network in Time using Feedback-Modulated Delay Loops

Deep neural networks are among the most widely applied machine learning ...
research
04/17/2018

Structured networks and coarse-grained descriptions: a dynamical perspective

This chapter discusses the interplay between structure and dynamics in c...
research
06/02/2019

Effect of two forms of feedback on the performance of the Rate Control Protocol (RCP)

The Rate Control Protocol (RCP) uses explicit feedback from routers to c...
research
11/03/2020

Levels of Coupling in Dyadic Interaction: An Analysis of Neural and Behavioral Complexity

From an enactive approach, some previous studies have demonstrated that ...

Please sign up or login with your details

Forgot password? Click here to reset