Hyperchaos & labyrinth chaos: Revisiting Thomas–Rössler systems

• 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
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2018.10.025

•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.