On wellposedness of generalized neural field equations with delay

2018/05/14 by Evgenii Burlakov, Burlakov, Evgenii, E. S. Zhukovskiy +5
Computer Science · Neuroscience · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Neural Networks Stability and Synchronization #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1805.06754

openalex publication_date 2018/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain conditions for existence of unique global or maximally extended solutions to generalized neural field equations. We also study continuous dependence of these solutions on the spatiotemporal integration kernel, delay effects, firing rate and prehistory functions.

Citations

• Dynamics of pattern formation in lateral-inhibition type neural fields

Related

• Time and State Dependent Neural Delay Differential Equations
• Global-in-time classical solutions and qualitative properties for the\n NNLIF neuron model with synaptic delay
• Well posedness and stationary solutions of a neural field equation with synaptic plasticity
• Numerical Solution of Stochastic Neural Fields with Delays
• Well-posedness and numerical analysis of an elapsed time model with strongly coupled neural networks