Existence and Stability of Square-Mean almost periodic Solutions to a Spatially Extended Neural Network with Impulsive Noise

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 (Unpublished)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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