Existence and nonexistence of traveling pulses in a lateral inhibition neural network

Existence and Stability of Traveling Fronts in a Lateral Inhibition Neural Network

We consider the existence and stability of traveling front solutions of a neural network consisting of a single–layer of neurons synaptically connected by lateral inhibition. For a specific ‘Mexican Hat’ coupling function, the existence condition for traveling fronts can be reduced to the solution of an algebraic system. Our work extends the existence of traveling fronts of the classic Amari mo...

Existence and Stability of Traveling Pulses in a Neural Field Equation with Synaptic Depression

We examine the existence and stability of traveling pulse solutions in a continuum neural network with synaptic depression and smooth firing rate function. The existence proof relies on geometric singular perturbation theory and blow-up techniques as one needs to track the solution near a point on the slow manifold that is not normally hyperbolic. The stability of the pulse is then investigated...

scour modeling piles of kambuzia industrial city bridge using hec-ras and artificial neural network

today, scouring is one of the important topics in the river and coastal engineering so that the most destruction in the bridges is occurred due to this phenomenon. whereas the bridges are assumed as the most important connecting structures in the communications roads in the country and their importance is doubled while floodwater, thus exact design and maintenance thereof is very crucial. f...

Existence of Traveling Waves in a Neural Model

In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of travelling wave fronts for a differential-integral equation modeling a neural network. Since then a number of authors have extended the model by adding an additional equation for a “recovery variable”, thus allowing the possibility of travelling pulse type solutions. In a recent paper G. Faye gave perhaps the first rigorous...

Existence and Nonexistence of Solutionsfor