Scientists show how chaotic systems can synchronize

Chaos is a real physical challenge. It is unpredictable. Out of control. Yet, researchers seem to have uncovered one of its secrets. They think to figure out how to put a little order. And this could help them better understand the functioning … of our brain!

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Observations in nanoscopy of mouse neurons allowed it to be discovered that the dendritic spines swelled and changed over a short period of time. © MaxPlanckSociety

The chaos. For the common of mortals, it is synonymous with confusion, disorder. Les physicists, they, have a very specific idea. A chaotic system behaves, according to those who study it, like an aléatoire system. He follows decisive laws well, his dynamics remain brought to change in a completely erroneous way. The famous « butterfly effect » which renders a chaotic system unpredictable. However, in the 1980s, researchers discovered that chaotic systems could synchronize. And today, des physicians from Bar-Ilan University (Israel) try to explain to us how it is possible.

To be well understood, precisely as a matter of fact, chaos is not always as chaotic as that. It sometimes seems to be attracted by a certain form of order. In its error and without ever going through the same point twice, a chaotic system can make me want to focus on a particular geometric figure. Physicists call this figure a strange attraction that forms the states of such a system in an abstract space called phases.

Curiously, the foreign attractors of chaotic systems generally appear to be composed of severalfractal structures – these structures with motifs that repeat themselves and again at different levels. Different sets of states of a strange attractor will be part of different fractals. Thus, even if the chaotic system rises erratically from one state to another, these fractures will remain stable throughout the chaotic activity of the dudit system.

To better understand the functioning of our brain

And it’s good émergence of stable fractals which constitute, according to researchers at the University of Bar-Ilan, the key element that allows chaotic systems to synchronize. Take for example two different chaotic systems. If some fracture structures of one of the systems begin to take on a similar shape to those of the other, a weak coupling is created. And to the extent that the coupling is strengthened, it acts as one light closure which constrained progressively more and more fractal structures to become identical. The complete synchronization of systems can only occur when chaotic systems are strongly coupled. A phenomenon that physicians have baptized “Topological synchronization”.

These results help to understand how synchronization and self-organization can emerge from systems that did not have these properties initially. Until then, physicists have become accustomed to studying similar chaotic systems whose parameters differ only very little. Thanks to topological synchronization, researchers have been able to extend the study of synchronization to extreme cases of chaotic systems that present themselves with very different parameters.

And if you think that these works are a little too abstract for you, know that the notion of topological synchronization can finally help us understand how the brain neurons one synchronizes with the other. There is indeed evidence that neuronal activity in our brain is chaotic. If this is the case, topological synchronization can describe how synchronization emits the vast amount of neuronal activity of thebrainby supporting stable fractal structures.

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