We have located links that may give you full text access.
The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions.
Journal of Mathematical Neuroscience 2017 October 27
Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounded domains. Neural field models do not require the specification of boundary conditions. Relatively little attention has been paid to the imposition of neural activity on the boundary, or to its role in inducing patterned states. Here we redress this imbalance by studying neural field models of Amari type (posed on one- and two-dimensional bounded domains) with Dirichlet boundary conditions. The Amari model has a Heaviside nonlinearity that allows for a description of localised solutions of the neural field with an interface dynamics. We show how to generalise this reduced but exact description by deriving a normal velocity rule for an interface that encapsulates boundary effects. The linear stability analysis of localised states in the interface dynamics is used to understand how spatially extended patterns may develop in the absence and presence of boundary conditions. Theoretical results for pattern formation are shown to be in excellent agreement with simulations of the full neural field model. Furthermore, a numerical scheme for the interface dynamics is introduced and used to probe the way in which a Dirichlet boundary condition can limit the growth of labyrinthine structures.
Full text links
Related Resources
Trending Papers
Heart failure with preserved ejection fraction: diagnosis, risk assessment, and treatment.Clinical Research in Cardiology : Official Journal of the German Cardiac Society 2024 April 12
Proximal versus distal diuretics in congestive heart failure.Nephrology, Dialysis, Transplantation 2024 Februrary 30
Efficacy and safety of pharmacotherapy in chronic insomnia: A review of clinical guidelines and case reports.Mental Health Clinician 2023 October
World Health Organization and International Consensus Classification of eosinophilic disorders: 2024 update on diagnosis, risk stratification, and management.American Journal of Hematology 2024 March 30
Get seemless 1-tap access through your institution/university
For the best experience, use the Read mobile app
All material on this website is protected by copyright, Copyright © 1994-2024 by WebMD LLC.
This website also contains material copyrighted by 3rd parties.
By using this service, you agree to our terms of use and privacy policy.
Your Privacy Choices
You can now claim free CME credits for this literature searchClaim now
Get seemless 1-tap access through your institution/university
For the best experience, use the Read mobile app