The name "labyrinth chaos" comes from the three-dimensional lattice generated in the phase space. The trajectories show anomalous diffusion and behave like a pseudo-random walk. This system is autocatalytic and has applications to ecology, evolution, and chemical reactions.
The system is defined by the equations
where the parameter represents frictional damping.
 R. Thomas, "Deterministic Chaos Seen in Terms of Feedback Circuits: Analysis, Synthesis, 'Labyrinth Chaos,'" International Journal of Bifurcation and Chaos, 9(10), 1999 pp. 1889–1905. doi:10.1142/S0218127499001383.
 R. Thomas, V. Basios, M. Eiswirth, T. Kruel, and O. E. Rössler, "Hyperchaos of Arbitrary Order Generated by a Single Feedback Circuit, and the Emergence of Chaotic Walks," Chaos, 14(3), 2004 pp. 669–674. doi:10.1063/1.1772551.