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#### Hyperchaos of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks

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##### Citation

Thomas, R., Basios, V., Eiswirth, M., Kruel, T., & Rössler, O. E. (2004). Hyperchaos
of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks.* Chaos,*
*14*(3), 669-674. doi:10.1063/1.1772551.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-0B5A-3

##### Abstract

It is shown that hyperchaos of order m (i.e., with m positive Lyapunov exponents) can be generated by a single feedback circuit in n = 2m + 1 variables. This feedback circuit is constructed such that, dividing phase space into hypercubes, it changes sign wherever the trajectory passes from one hypercube into an adjacent one. Letting the negative diagonal elements in the Jacobian tend to zero, the dynamics becomes conservative. Instead of chaotic attractors, unbounded chaotic walks are then generated. Here we report chaotic walks emerging from a continuous system rather than the well known chaotic walks present in "Lorentz gas" and "couple map lattices."