Translartion. Region: Russians Fedetion –
Source: State University Higher School of Economics – State University Higher School of Economics –
Researchers fromInternational Laboratory of Dynamic Systems and Applications HSE University – Nizhny Novgoroddeveloped a theory that allows us to prove with mathematical precision the existence of stable chaotic behavior in networks of interacting elements. The work opens up new possibilities for studying complex dynamic processes in neuroscience, biology, medicine, chemistry, optics and other fields. The results of the study have been accepted for publication in the leading international scientific journal Physical Review Letters. The results of the study can beget acquaintedin the Arxiv.org archive.
In scientific terminology, chaos does not mean disorder, but dynamics that are extremely sensitive to the slightest changes. In such modes, the system’s behavior becomes unpredictable, which in some cases turns out to be useful. For example, in neuroscience, stable chaos helps prevent excessive synchronization of neurons and, as a result, epileptic seizures. In artificial intelligence algorithms, chaotic modes help improve the efficiency of learning.
Chaotic dynamics are also used to describe behavioral and economic cycles and help make more accurate short-term forecasts. However, until recently, the question remained open: how to understand whether the observed dynamics are truly chaotic, or just a temporary phenomenon, followed by stabilization of the system?
Scientists from the National Research University Higher School of Economics – Nizhny Novgorod, Professor Alexey Kazakov and postgraduate students Efrosinia Karatetskaya and Klim Safonov, together with Professor Dmitry Turaev from Imperial College London, were able to answer this question by applying the concept of pseudo-hyperbolicity.
Professor Turaev took part in the creation of this concept together with the Nizhny Novgorod mathematician Leonid Shilnikov. This property of the system excludes the transition to a stable state and guarantees the preservation of chaotic behavior, even if the system is affected by small external disturbances. By checking the conditions of pseudohyperbolicity, the researchers proved that networks of four or more identical interacting oscillators can demonstrate stable chaos under certain functions of the connections between the elements.
Moreover, the authors constructed numerical maps of the regions of existence of stable and unstable chaos and described different types of chaotic attractors, including two-winged and four-winged analogues of the classical Lorenz attractor.
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