This text provides an introduction to the exciting new developments in chaos and related
topics in nonlinear dynamics, including the detection and quantification of chaos in …

Recurrent excitation is experimentally well documented in cortical populations. It provides
for intracortical excitatory biases that linearize negative feedback interactions and induce …

Both academic and applied researchers studying financial markets and other economic
series have become interested in the topic of chaotic dynamics. The possibility of chaos in …

By using the method of orthogonal polynomials, we analyze the statistical properties of
complex eigenvalues of random matrices describing a crossover from Hermitian matrices …

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 …

Almost all artificial neural networks are by default fully connected, which often implies a high
redundancy and complexity. Little research has been devoted to the study of partially …

The aim of the present paper is to study the effects of Hebbian learning in random recurrent
neural networks with biological connectivity, ie sparse connections and separate …

Additional Resource Materials Human behavior would not be interesting to us if it remained
the same from one moment to the next. Moreover, we tend to be sensitive to changes in …

We consider an ensemble of large non-Hermitian random matrices of the form H ̂+ i A ̂ s,
where H ̂ and A ̂ s are Hermitian statistically independent random N× N matrices. We …

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