https://doi.org/10.1140/epjp/s13360-021-01662-y
Regular Article
Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals
Dynamical system with a self-organising vector field
1
Department of Mathematics, Loughborough University, LE11 3TU, Loughborough, UK
2
Mathematisches Institut, University of Tübingen, 72074, Tübingen, Germany
Received:
13
February
2021
Accepted:
9
June
2021
Published online:
5
July
2021
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.
The visit of PEK to Loughborough University was supported by London Mathematical Society.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.