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Hyperchaos and its control in two-level quantum oscillators lattice

Andrei Andreev
The behavior of the square lattices of coupled two-level quantum oscillators is investigated. As quantum oscillators, we use the model of Rydberg atoms obtained using the approximation of a fully factorized density matrix. To investigate the behavior of the system the Lyapunov exponents spectra are calculated. Chaos and hyperchaos in the systems are revealed. It was shown that
the number of positive Lyapunov exponents almost linearly
depends on the number of atoms in the system, at a rate suggesting that adding three atoms leads to the appearance
of an additional positive Lyapunov exponent. Using an external parametric effect and continuous feedback is suggested to control the complicated dynamics in the system. Using continuous feedback allows reducing the number of positive Lyapunov exponents from 3 to only 2 while introducing external parametric influence into the system allows reducing their number down to 0
and completely suppresses hyperchaos.
CYBERNETICS AND PHYSICS, Vol. 8, No. 3. 2019, 93-97. https://doi.org/10.35470/2226-4116-2019-8-3-93-97
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