29 citations · 32 across the 4 of their papers we have counts for
6 papers
Existence and stability of periodic solutions in a neural field equation
Karina Kolodina, Vadim Kostrykin, Anna Oleynik
We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption…
Greedy Gauss-Newton algorithm for finding sparse solutions to nonlinear underdetermined systems of equations
Mårten Gulliksson, Anna Oleynik
We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search…
Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity
Anna Oleynik, Arcady Ponosov, Vadim Kostrykin +1
We study the existence of fixed points to a parameterized Hammertstain operator $\cH_β,$ with sigmoid type of nonlinearity. The parameter indicates th…
Iterative Schemes for Bump Solutions in a Neural Field Model
Anna Oleynik, Arcady Ponosov, John Wyller
We develop two iteration schemes for construction of localized stationary solutions (bumps) of a one-population Wilson-Cowan model with a smoothed Heaviside firing rate function. T…
An intermediate value theorem in ordered Banach spaces
Vadim Kostrykin, Anna Oleynik
We consider a monotone increasing operator in an ordered Banach space having and as a strong super- and subsolution, respectively. In contrast with the well studied cas…
On the Existence of Unstable Bumps in Neural Networks
Vadim Kostrykin, Anna Oleynik
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 of bump…