Scientists have discovered how to bring some order to a chaotic system, thus opening up a number of possibilities for a better understanding of biological systems and even brain mechanisms.
Researchers from Bar-Ilan University in Israel, led by Dr. nir lahav, have discovered how chaotic systems can evolve towards order and allow themselves to be dominated by fractals, the geometric code of nature. The results have been published in the journal Scientific Reports.
Chaotic systems represent a form of organization existing in nature. They are defined as random because, although they can follow deterministic laws, they are very sensitive to initial variations and enter an unpredictable drift.
That means that if you alter some of the parameters of a chaotic system, the end result is completely different from the original.
There are many examples of chaotic systems and one of the clearest is the climate, well known through the so-called “butterfly effect”, which has its origins in the study of meteorology.
The weather is a chaotic system because the weak flapping of a butterfly’s wings at one point on the globe can, in the long run, prevent a storm from forming on the other side of the globe. For this reason it has been thought that the chaos theory could lead to technology capable of controlling the weather.
tendency to order
It is also known that chaotic systems are sometimes attracted to some kind of order and tend to form geometric figures.
Within these dynamic systems a set of points called strange attractorswhich “seduce” the chaotic system and induce it to take the form of a geometric figure.
Those attractors emerge formed by fractal structures: they remain adrift within a chaotic system, which by nature is alien to any kind of ordered structure.
According to researchers at Bar-Ilan University, these stable fractals allow chaotic systems to synchronize with each other, something that had already been discovered in 1980 and was still pending explanation.
This process, according to the new research, begins when the fractal structures of the strange attractors begin to assimilate with each other, subsequently producing synchronization between them.
If the fractal structures of two or more attractors end up becoming totally identical, both systems become fully synchronized. The authors emphasize that it is a gradual and not a sudden process.
Then it reaches topological synchronizationin which the multifractal structure of a strange attractor approaches that of the other, until the multifractal structures of both attractors end up being the same structure, the authors of this research write in their article.
Israeli researchers have called this culminating process Zipper Effect: reveals that chaotic synchronization is a continuous process that can be described.
Described mathematically, the zipper effect reveals that, as the coupling between systems becomes stronger, the fractals gradually merge with each other until they end up being the same. That means that topological timing, understood as a microscopic description of timing, has a kind of expansive wave.
The Israeli team wants to go even further: it has extended the study of synchronization to extreme cases of chaotic systems with large differences between their parameters (the least studied), to check if topological synchronization also works in extreme situations.
However, the authors of this research suggest that topological synchronization should be studied further and that additional studies should be carried out to continue and validate the results presented in this work.
brain and chaos
They also add that one application of these results is to determine how much synchronization a physical system has and where, in what phase space, it occurred.
For this reason, it is considered that the topological synchronization established in this study could shed light, among other applications, on how neurons in the brain synchronize with each other for any cognitive function.
In 2019, researchers from the blue brain projectat the Federal Polytechnic School of Lausanne, discovered how the brain finds order within the chaos in which neurons often position themselves when they want to communicate with each other.
The authors of the new research consider in this regard that topological synchronization can describe how this order within chaos in the vast neuronal activity of the brain, and they specify that this emergence depends on the stable fractal structures that they suppose are also present in the neuronal activity. An interesting clue that opens new avenues for neuroscientific research.
Topological synchronization of chaotic systems. Nir Lahav et al. Scientific Reports, Volume 12, Article number: 2508 (2022).