Dynamical systems on generalised Klein bottles

Grindrod, Peter and Yim, Ka Man ORCID: https://orcid.org/0000-0003-4736-3151 2025. Dynamical systems on generalised Klein bottles. Entropy 27 (2) , 119. 10.3390/e27020119

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Abstract

We propose a high-dimensional generalisation of the standard Klein bottle extending beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state spaces, which can provide a rich source of examples for future investigations. We consider a class of high-dimensional dynamical systems that model distributed information processing within the human cortex, which may be capable of exhibiting some Klein bottle symmetries. We deploy topological data analytic methods in order to analyse their resulting dynamical behaviour and suggesting future challenges.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: https://creativecommons.org/licenses/by/4.0/, Start Date: 2025-01-24
Publisher:	MDPI
Date of First Compliant Deposit:	4 February 2025
Date of Acceptance:	29 December 2024
Last Modified:	04 Feb 2025 11:30
URI:	https://orca.cardiff.ac.uk/id/eprint/175901

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