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Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals

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journal contribution
posted on 09.07.2021, 08:26 by Natalia JansonNatalia Janson, Peter E Kloeden
We investigate the robustness with respect to random stimuli of a dynamical system with a plastic self-organising vector field, previously proposed as a conceptual model of a cognitive system and inspired by the self-organised plasticity of the brain. This model of a novel type consists of an ordinary differential equation subjected to the time-dependent “sensory” input, whose time-evolving solution is the vector field of another ordinary differential equation governing the observed behaviour of the system, which in the brain would be neural firings. It is shown that the individual solutions of both these differential equations depend continuously over finite time intervals on the input signals. In addition, under suitable uniformity assumptions, it is shown that the non-autonomous pullback attractor and forward omega limit set of the given two-tier system depend upper semi-continuously on the input signal. The analysis holds for both deterministic and noisy input signals, in the latter case in a pathwise sense.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

The European Physical Journal Plus

Volume

136

Issue

7

Publisher

Springer

Version

VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

09/06/2021

Publication date

2021-07-05

Copyright date

2021

eISSN

2190-5444

Language

en

Depositor

Dr Natalia Janson. Deposit date: 17 June 2021

Article number

720