A group of scientists from Russia and Europe has mathematically created a model showing that chaos in systems where elements are interconnected can be stable and last for a long time. This research was conducted by Professor Dmitry Turaev from Imperial College London. He used a special method (pseudo-hyperbolicity) to understand whether the disorder in the system is true chaos or just a temporary problem, after which everything will return to normal. This was reported by the press service of the Higher School of Economics.
Chaos in systems is a state where even small changes in conditions lead to unpredictable consequences. This behavior is everywhere: it helps describe fluctuations in financial markets, protects the brain from excessive synchronization of neurons, and improves the learning of artificial intelligence algorithms. However, it remained unclear whether the chaos would last long or the system would soon stabilize. Scientists solved this problem by applying the concept of pseudo-hyperbolicity — an approach created by Turaev and mathematician Leonid Shilnikov more than a decade ago.
Until recently, the question remained open: how to understand whether the observed dynamics are truly chaotic, or is it just a temporary phenomenon, followed by stabilization of the system? Russian scientists were able to answer this question by applying the concept of pseudo-hyperbolicity.
Scientists studied special elements (attractors) that help understand how chaotic systems behave. They created diagrams that show when chaos in groups of four or more elements can remain stable. These models helped them create "chaos maps" that show where disorder remains and where it disappears, depending on how the elements interact with each other.
The new research opens new horizons in understanding chaos and its stability, which may have important implications for neuroscience, biology, medicine, chemistry, and optics.
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