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Hyperchaos of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks
René Thomas1, Vasileios Basios, Markus Eiswirth
1Center for Nonlinear Phenomena and Complex Systems, Universite Libre de Bruxelles, C.P. 231, Bd. Du Triomphe, 1050 Brussels, Belgium.
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."
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