Labyrinth chaos: Revisiting the elegant, chaotic and hyperchaotic walks

TL;DR

This paper revisits labyrinth chaos, exploring single and coupled systems that exhibit complex, hyperchaotic, and chimera-like behaviors, highlighting their unique properties and implications for understanding chaotic dynamics.

Contribution

It introduces the study of coupled labyrinth chaos systems exhibiting chimera-like states and analyzes their properties, expanding understanding of hyperchaotic and chaotic trajectories.

Findings

Coupled labyrinth chaos systems can exhibit chimera-like states.

Labyrinth chaos systems have volume-preserving yet non-force-conservative properties.

Single labyrinth walks systems display complex, hyperchaotic trajectories.

Abstract

Labyrinth chaos was discovered by Otto R\"ossler and Ren\'e Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walks system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behaviour, reminiscent of chimera-like states, a peculiar synchronisation phenomenon. We discuss the properties of the single labyrinth walks system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, what amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walks system by showing that even though it is volume-preserving, it is not force-conservative.