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ISS-Stabilization of Delayed Neural Fields by Small-Gain Arguments

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Part of the Advances in Delays and Dynamics book series (ADVSDD,volume 10)

Abstract

This chapter addresses the robust stabilization of neuronal populations modeled as delayed neural fields. These models are integro-differential equations representing the spatio-temporal activity of cerebral structures and take into account the non-instantaneous communication between neurons. It is assumed that the stimulation signal impacts only a subpopulation, referred to as the “controlled” population. We show that, if the synaptic coupling within the “uncontrolled” population is below some explicit threshold, then a proportional feedback relying only on measurements of the controlled subpopulation activity succeeds in ensuring robust stability of the overall population. These theoretical developments rely on an extension of the input-to-state stability (ISS) property, and associated small-gain results, to spatio-temporal delayed dynamics.

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  • DOI: 10.1007/978-3-030-11554-8_5
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Correspondence to Antoine Chaillet .

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Chaillet, A., Detorakis, G.I., Palfi, S., Senova, S. (2019). ISS-Stabilization of Delayed Neural Fields by Small-Gain Arguments. In: Valmorbida, G., Seuret, A., Boussaada, I., Sipahi, R. (eds) Delays and Interconnections: Methodology, Algorithms and Applications. Advances in Delays and Dynamics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-11554-8_5

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