Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic
neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in …

What happens in our brain when we make a decision? What triggers a neuron to send out a
signal? What is the neural code? This textbook for advanced undergraduate and beginning …

Neurons in the brain communicate by short electrical pulses, the so-called action potentials
or spikes. How can we understand the process of spike generation? How can we …

We present some recent investigations resulting from the modeling of neural networks as
dynamical systems, and deal with the following questions, adressed in the context of specific …

This article is part of the Physical Review Research collection titled Physics of
Neuroscience. Recurrent networks are widely used as models of biological neural circuits …

This paper studies the hydrodynamic limit of a stochastic process describing the time
evolution of a system with N neurons with mean-field interactions produced both by …

We study theoretically the dimensional crossover from a three-dimensional elongated
condensate to a one-dimensional condensate as the transverse degrees of freedom get …

Recurrent networks of non-linear units display a variety of dynamical regimes depending on
the structure of their synaptic connectivity. A particularly remarkable phenomenon is the …

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

We derive rigorous results describing the asymptotic dynamics of a discrete time model of
spiking neurons introduced in Soula et al.(Neural Comput. 18, 1, 2006). Using symbolic …