Hyperchaos & Labyrinth chaos: Revisiting Thomas-Rössler systems

Abstract: We consider a multi-dimensional extension of the Thomas-R\"ossler (TR) 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 a spatio-temporal behaviour, reminiscent of chimera states. The novelty here being that its underlying mechanism is based on "chaotic walks" discovered by Ren\'e Thomas during the course of his investigations on what he called Labyrinth Chaos. We briefly review the main properties of TR 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 Ren\'e Thomas' memorable influence and interaction with the authors as we dedicate this work to his memory.