Postlethwaite, CM and Sturman, R (2022) Stability of heteroclinic cycles in ring graphs. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32 (6). 063104. ISSN 1054-1500
Abstract
Networks of interacting nodes connected by edges arise in almost every branch of scientific inquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical systems. These invariant subspaces can result in the appearance of robust heteroclinic cycles, which would otherwise be structurally unstable. Typically, the dynamics near a stable heteroclinic cycle is non-ergodic: mean residence times near the fixed points in the cycle are undefined, and there is a persistent slowing down. In this paper, we examine ring graphs with nearest-neighbor or nearest-m-neighbor coupling and show that there exist classes of heteroclinic cycles in the phase space of the dynamics. We show that there is always at least one heteroclinic cycle that can be asymptotically stable, and, thus, the attracting dynamics of the network are expected to be non-ergodic. We conjecture that much of this behavior persists in less structured networks and as such, non-ergodic behavior is somehow typical.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Jun 2022 08:08 |
Last Modified: | 25 Jun 2023 23:00 |
Status: | Published |
Publisher: | American Institute of Physics |
Identification Number: | 10.1063/5.0088856 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:187865 |