Absolute Stability and Complete Synchronization in a Class of Neural Fields Models

Neural fields are an interesting option for modelling macroscopic parts of the cortex involving several populations of neurons, like cortical areas. Two classes of neural field equations are considered: voltage and activity based. The spatio-temporal behaviour of these fields is described by nonlinear integro-differential equations. The integral term, computed over a compact subset of Rq, q = 1, 2, 3, involves space and time varying, possibly non-symmetric, intra-cortical connectivity kernels. Contributions from white matter afferents are represented as external input. Sigmoidal nonlinearities arise from the relation between average membrane potentials and instantaneous firing rates. Using methods of functional analysis, we characterize the existence and uniqueness of a solution of these equations for general, homogeneous (i.e. independent of the spatial variable), and spatially locally homogeneous inputs. In all cases we give sufficient conditions on the connectivity functions for the...

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Olivier D. Faugeras, François Grimbert, Jean-Jacques E. Slotine
• Keywords: Equations, Neural Field, Neural Field Equations, SIAMAM 2008