Evgenii Burlakov, Evgeny Zhukovskiy, Arcady Ponosov, and John Wyller

Existence, Uniqueness and Continuous Dependence on Parameters of Solutions to Neural Field Equations

abstract:
We obtain conditions for the existence and uniqueness of solutions to generalized neural field equations involving parameterized measure. We study continuous dependence of these solutions on the spatiotemporal integration kernel, delay effects, firing rate, external input and measure. We also construct the connection between the delayed Amari and Hopfield network models.

Mathematics Subject Classification: 46T99, 45G10, 49K40, 92B20

Key words and phrases: Neural field equations, Hopfield networks, well-posedness