The tools of dynamical systems theory are having an increasing impact on our
understanding of patterns of neural activity. In this tutorial chapter we describe how to build …

We study the existence and continuous dependence of stationary solutions of the one-
population Wilson–Cowan model on the steepness of the firing rate functions. We …

The first goal of this article is to introduce a new type of p-adic reaction-diffusion cellular
neural network with delay. We study the stability of these networks and provide numerical …

We study existence and continuous dependence of the solutions to the Hammerstein
operator equation under the transition from continuous nonlinearities in the Hammerstein …

We study the existence of fixed points to a parameterized Hammerstein operator H β,
β∈(0,∞], with sigmoid type of nonlinearity. The parameter β<∞ indicates the steepness of …

This paper is devoted to research in mathematical neurobiology; its main purpose is to
establish the connection between approaches to the modeling of neural fields based on …

We study the neuronal field equation, a nonlinear integro-differential equation of
Hammerstein type. By means of the Amann three fixed point theorem we prove the existence …

We study numerically single bump solutions of a homogenized Amari equation with periodic
microvariation. Two attempts are made to detect single bumps that depend on the …

The first goal of this article is to introduce a new type of p" adic reaction" diffusion cellular
neural network with delay. We study the stabil" ity of these networks and provide numerical …

The need to understand the neural field activity for realistic living systems is a current
challenging task in neuroscience. For several decades, neural fields have been studied and …