Existence and Uniqueness of Traveling Fronts in Lateral Inhibition Neural Fields with Sigmoidal Firing Rates
نویسندگان
چکیده
منابع مشابه
Neural fields with sigmoidal firing rates: approximate solutions
Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for sta...
متن کاملExistence 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...
متن کاملSpeed of traveling fronts in a sigmoidal reaction-diffusion system.
We study a sigmoidal version of the FitzHugh-Nagumo reaction-diffusion system based on an analytic description using piecewise linear approximations of the reaction kinetics. We completely describe the dynamics of wave fronts and discuss the properties of the speed equation. The speed diagrams show front bifurcations between branches with one, three, or five fronts that differ significantly fro...
متن کاملTraveling fronts in porous media: existence and a singular limit
We consider a model for the propagation of a subsonic detonation wave through a porous medium introduced by Sivashinsky [8]. We show that it admits travelling wave solutions that converge in the limit of zero temperature diffusivity to the travelling fronts of a reduced system constructed in [6].
متن کاملGeneralized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability
We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translates of the front. In the case of stationary ergodic reactions the fronts are proved to propagat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2020
ISSN: 1536-0040
DOI: 10.1137/20m1311697