Bonaccorsi, Stefano and Ziglio, Giacomo (2011) Existence and Stability of Square-Mean almost periodic Solutions to a Spatially Extended Neural Network with Impulsive Noise. UNSPECIFIED. (Unpublished)
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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 diusion process in the network. This paper aims to throw some light on time-varying, stochastically perturbed, neuronal networks. We show that when the coecients oscillate around a reference value, with ascillations 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 mean square norm for all times.
| Item Type: | Departmental Technical Report |
|---|---|
| Department or Research center: | Mathematics |
| Subjects: | Q Science > QA Mathematics > QA276 Mathematical Statistics Q Science > QA Mathematics > QA273 Probabilities Q Science > QA Mathematics > QA374.7 Partial differential equations |
| Uncontrolled Keywords: | diffusion equations on networks, stochastic impulses, almost periodic solutions |
| Report Number: | UTM 746 |
| Repository staff approval on: | 25 Jul 2011 |
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