Hyperchaos & labyrinth chaos: Revisiting Thomas–Rössler systems

•Revisiting Thomas’ work on Labyrinth Chaos and Hyperchaos.•Extending Thomas’ and Rössler’s work to a spatio-temporal setting.•Detection of chimera states, their necessary conditions and properties.•Proposal of a novel mechanism for chimera states based on Labyrinth Chaos. We consider a multidimensi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of theoretical biology 2019-01, Vol.460, p.153-159
Main Authors: Basios, Vasileios, Antonopoulos, Chris G.
Format: Article
Language:English
Subjects:
Chaos
Chimera-like states
Complex periodic oscillations
Feedback, Physiological
Humans
Hyperchaos
Labyrinth chaos
Networks
Nonlinear Dynamics
René Thomas
Spatio-Temporal Analysis
Spatio-temporal behaviour
Thomas-Rössler systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•Revisiting Thomas’ work on Labyrinth Chaos and Hyperchaos.•Extending Thomas’ and Rössler’s work to a spatio-temporal setting.•Detection of chimera states, their necessary conditions and properties.•Proposal of a novel mechanism for chimera states based on Labyrinth Chaos. We consider a multidimensional extension of Thomas–Rössler systems, that was inspired by Thomas’ earlier work on biological feedback circuits, and we report on our first results that shows its ability to sustain spatio-temporal behaviour reminiscent of chimera states. The novelty here is that its underlying mechanism is based on “chaotic walks” discovered by Thomas during the course of his investigations on what he called Labyrinth Chaos. We briefly review the main properties of these systems and their chaotic and hyperchaotic dynamics and discuss the simplest way of coupling, necessary for this spatio-temporal behaviour that allows the emergence of complex dynamical behaviours. We also recall Thomas’ memorable influence and interaction with the authors as we dedicate this work to his memory.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2018.10.025