On ring solutions of neural field equations

DOI10.20310/2686-9667-2021-26-136-363-371OpenAlexW4205782416MaRDI QIDQ5092861

Evgenii Burlakov, Ramid Atmaniya, Ivan Nikolaevich Mal'Kov

Publication date: 26 July 2022

Published in: Russian Universities Reports. Mathematics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vtamu237

zbMATH Keywords

existence of solutionsapproximation of solutionsring solutiontwo-dimensional neural field equation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Theoretical approximation of solutions to integral equations (45L05)

Cites Work

• Stationary solutions of continuous and discontinuous neural field equations
• On the properties of nonlinear nonlocal operators arising in neural field models
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Existence and stability of local excitations in homogeneous neural fields
• Two-bump solutions of Amari-type models of neuronal pattern formation
• On inclusions arising in neural field modeling
• On continuous and discontinuous models of neural fields
• Waves, bumps, and patterns in neural field theories
• Spatiotemporal dynamics of continuum neural fields
• Multiple Bumps in a Neuronal Model of Working Memory
• PDE Methods for Nonlocal Models
• On connection between continuous and discontinuous neural field models with microstructure: II. Radially symmetric stationary solutions in 2D (“bumps”)
• Stimulus-Locked Traveling Waves and Breathers in an Excitatory Neural Network

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