Labyrinth Chaos

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.


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The system is defined by the equations
where the parameter represents frictional damping.
[1] 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.
[2] 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.
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