Scientists show how chaotic systems can synchronize

Chaos is a real challenge to physics. He is unpredictable. Out of control. However, researchers seem to have pierced one of its secrets. They think they have figured out how to bring some order to it. And this could help them better understand how our brains work!

Chaos. For ordinary mortals, it is synonymous with confusion and disorder. The physicists, they have a very precise idea of ​​it. A chaotic system behaves, according to those who study it, like a random system. It may well follow deterministic laws, but its dynamics are bound to change in a totally erratic way. The famous ” butterfly Effect » which makes a chaotic system unpredictable. However, in the 1980s, researchers discovered that sometimes chaotic systems synchronize. And today, Bar-Ilan University physicists (Israel) are trying to explain to us how this is possible.

To fully understand, let us specify that in reality, chaos is not always so chaotic as that. He sometimes seems to be drawn to some form of order. In its wanderings and without ever passing twice through the same point, a chaotic system can pretend to want to move towards a particular geometric figure. Physicists call this figure formed by the states of such a system in an abstract space called phases a strange attractor.

Curiously, the strange attractors of chaotic systems generally appear composed of severalfractal structures – those structures with patterns that repeat themselves again and again at different scales. Different sets of states of a strange attractor will be part of different fractals. Thus, although the chaotic system jumps erratically from one state to another, these fractals will remain stable throughout the chaotic activity of said system.

To better understand how our brain works

And it is well emergence stable fractals which, according to researchers at Bar-Ilan University, is the key element that allows chaotic systems to synchronize. Take for example two different chaotic systems. If a few fractal structures of one of the systems begin to take a similar shape to those of the other, a weak coupling is created. And as the coupling grows stronger, it acts as a zipper which is gradually forcing more and more fractal structures to become identical. Full synchronization of systems can only occur when chaotic systems are strongly coupled. A phenomenon that physicists have named “topological synchronization”.

These results help to understand how synchronization and self-organization can emerge from systems that initially lacked these properties. Until then, physicists used to study similar chaotic systems whose parameters differ only very little. Thanks to topological synchronization, the researchers succeeded in extending the study of synchronization to the extreme cases of chaotic systems which present themselves with very different parameters.

And if you think these works are a little too abstract for you, know that the notion of topological synchronization could ultimately help us understand how the brain neurons synchronize with each other. There is indeed evidence that neural activity in our brain is chaotic. If so, topological synchronization may describe how synchronization emerges from the vast neural activity of thebrainrelying on stable fractal structures.