Labyrinth Chaos & Labyrinth Walks: Elegant Chaos and Chaotic Walks without Attractors

Labyrinth chaos was discovered by Otto Rossler and Rene Thomas in their endeavour to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows.
This is a generic and minimal model of a dynamical system which turned out that, even though it is simple, it is full of surprising properties. Simple and elegant as it is, it still holds great promise for elucidating aspects of chaotic dynamics that are not evident in other systems.
Our work highlights the incredible riches of this system in its disconcerting simplicity and importance in the context of dynamical systems and in other fields.
As an example, we consider an array of coupled labyrinth chaos systems found to exhibit complex chaotic behaviour reminiscent of chimera-like states. We discuss a peculiar synchronization phenomenon due to the properties of the labyrinth walks as well as their ability of to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories.
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.