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We consider a conductance-based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distributi...
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being t...
Development of effective and plausible numerical tools is an imperative task for thorough studies of nonlinear dynamics in life science applications.
Physical and physiological invariance laws, in particular time invariance and local symmetry, are at the outset of an abstract model. Harmonic analysis and Lie theory are the mathematical prerequisites for its...
We study the neural field equations introduced by Chossat and Faugeras to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, th...
We consider the constrained optimization of excitatory synaptic input patterns to maximize spike generation in leaky integrate-and-fire (LIF) and theta model neurons. In the case of discrete input kicks with a...
We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic...
In this paper, we consider neural field equations with space-dependent delays. Neural fields are continuous assemblies of mesoscopic models arising when modeling macroscopic parts of the brain. They are modele...
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