Mathematicians from HSE Campus in Nizhny Novgorod Prove Existence of Robust Chaos in Complex Systems
Researchers from the International Laboratory of Dynamical Systems and Applications at the HSE Campus in Nizhny Novgorod have developed a theory that enables a mathematical proof of robust chaotic dynamics in networks of interacting elements. This research opens up new possibilities for exploring complex dynamical processes in neuroscience, biology, medicine, chemistry, optics, and other fields. The study findings have been accepted for publication in Physical Review Letters, a leading international journal. The findings are available on arXiv.org.
In scientific terms, chaos does not imply disorder but rather refers to dynamics that are extremely sensitive to even the slightest changes. Under these conditions, the system exhibits unpredictable behaviour, which can be useful in certain contexts. For example, in neuroscience, sustained chaotic activity helps prevent excessive synchronisation of neurons, thereby reducing the risk of epileptic seizures. Chaotic modes in artificial intelligence algorithms can contribute to more efficient training.
Chaotic dynamics are also used to describe behavioural and economic cycles, helping improve the accuracy of short-term forecasts. However, until recently, a key question remained: how can we determine whether the observed dynamics are truly chaotic, or merely a temporary phenomenon that eventually leads to system stabilisation?
Prof. Alexey Kazakov and doctoral students Efrosiniia Karatetskaia and Klim Safonov at the HSE Campus in Nizhny Novgorod, in collaboration with Dmitry Turaev, Professor at Imperial College London, were able to answer this question by applying the concept of pseudohyperbolicity.
Professor Turaev contributed to the development of this concept alongside Nizhny Novgorod mathematician Leonid Shilnikov. This property of the system prevents its transition to a stable state and ensures the robustness of chaotic behaviour, even in the presence of minor external disturbances. By testing the conditions of pseudohyperbolicity, the researchers demonstrated that networks of four or more identical interacting oscillators can exhibit robust chaos, given certain functions governing connections between the elements.
Furthermore, the authors constructed numerical maps outlining the regions of stable and unstable chaos and described various types of chaotic attractors, including two-winged and four-winged analogues of the classical Lorenz attractor.
The study was carried out within the framework of the HSE Centres of Excellence project and the HSE University Basic Research Programme intercampus project.
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