Existence and stability of square-mean almost periodic solutions to a spatially extended neural network with impulsive noise
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Abstract.
Our work is concerned with a neural network with n nodes, where the activity of the k-th cell depends on external, stochastic inputs as well as the coupling generated by the activity of the adjacent cells, transmitted through a diffusion process in the network. This paper aims to throw some light on time-varying, stochastically perturbed, neuronal networks. We show that when the coefficients oscillate around a reference value, with oscillations that are almost periodic and suitably small in percentage, then there exists a unique solution for the system, that is almost periodic and uniformly bounded in the square-mean norm for all times.
Funding source: Provincia Autonoma di Trento (P.A.T.)
Award Identifier / Grant number: Project NeSt
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Gegenbauer random fields
- Existence and stability of square-mean almost periodic solutions to a spatially extended neural network with impulsive noise
- Stochastic controls of relaxed-singular problems
- Large deviations for integrals of telegraph processes type
- The Cauchy problem for the heat equation with a random right side
Articles in the same Issue
- Frontmatter
- Gegenbauer random fields
- Existence and stability of square-mean almost periodic solutions to a spatially extended neural network with impulsive noise
- Stochastic controls of relaxed-singular problems
- Large deviations for integrals of telegraph processes type
- The Cauchy problem for the heat equation with a random right side
