Synchronizing a 2D continuum of two populations of neural masses

Olivier Faugeras,Jean-Jacques Slotine

doi:10.1186/1471-2202-8-s2-p178

Olivier Faugeras, Jean-Jacques Slotine

Open Access

https://doi.org/10.1186/1471-2202-8-s2-p178

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Abstract

Background Neural field models of firing rate activity have played a major role in developing an understanding of the dynamics of neural tissues [1]. In this paper we study the possibility of synchronizing a two-dimensional neural field of excitatory and inhibitory layers of neural masses. This is the first step toward an investigation of the properties of visual areas in man and monkey. Each population is described by its post-synaptic potential (PSP), hence the state space is a two-dimensional function defined on the 2D continuum. The field is modeled by an integro-differential equation. At a given point in the continuum this equation models the synaptic integration of the neural mass through a linear term and the contributions of its neighbors to the variation of its PSP through a spatial integration of their firing rates weighted by a connectivity function. The firing rates are classically related to the PSPs through sigmoidal functions.

Highlights

Neural field models of firing rate activity have played a major role in developing an understanding of the dynamics of neural tissues [1]
Each population is described by its post-synaptic potential (PSP), the state space is a two-dimensional function defined on the 2D continuum
We provide sufficient conditions on the connectivity matrix of the neural field for the existence of an homogeneous solution

Summary

Background

Neural field models of firing rate activity have played a major role in developing an understanding of the dynamics of neural tissues [1]. In this paper we study the possibility of synchronizing a two-dimensional neural field of excitatory and inhibitory layers of neural masses. This is the first step toward an investigation of the properties of visual areas in man and monkey. Each population is described by its post-synaptic potential (PSP), the state space is a two-dimensional function defined on the 2D continuum. At a given point in the continuum this equation models the synaptic integration of the neural mass through a linear term and the contributions of its neighbors to the variation of its PSP through a spatial integration of their firing rates weighted by a connectivity function. The firing rates are classically related to the PSPs through sigmoidal functions

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Conclusion

Coombes S