Topological synchronization of chaotic systems

Can we find order in chaos? Physicists have shown for the first time that chaotic systems can be synchronized by stable structures. Flaws are shapes with patterns which repeat over and over again in different scales. When chaotic systems are coupled, the structures of the different systems will start to form the same shape.

The systems will eventually become identical if the systems are strongly coupled. These findings help us understand how chaotic systems and biological systems can emerge from systems that do not have these properties.

Chaos is one of the biggest challenges in physics. Chaos in physics has a specific meaning. Chaotic systems are like random systems. They follow deterministic laws, but their dynamics will change in different ways. Thebutterfly effect makes their future behavior unpredictable like the weather system.

Order can be found in chaotic systems. A strange attractor emerges from chaotic activity. Every chaotic system will stay in this pattern if enough time passes. The strange thing about these patterns is that they are made up of structures with the same patterns repeating over and over again in different scales of the fractal, like a branching structure of a tree. Weird attractors are usually composed of multiple structures. The system will jump from state to state, but the system will stay stable because of the different sets of states in the system.

Chaos systems seem to defy the rules. Two chaotic systems can't be synchronized and have the same activity because of their erratic behavior. Physicists discovered in the 80's that chaotic systems do sync. How can that be?

A group of physicists from Israel's Ilan University published a study in the journal Scientific Reports that suggests a new answer to the question. According to the research, the emergence of the stable fractals is the key element that gives chaotic systems the ability to sync. They showed that when chaotic systems are coupled, the structures start to integrate. The systems will eventually become identical if the systems are strongly coupled. They called it Topological Synchronization. In lowcoupling, a small amount of the structures will become the same as the systems grow.

The physicists were surprised to find that there is a specific trait for the process of how the two systems are related. The process in chaotic systems maintains the same form. When the two chaotic systems are not weakly coupled, the process usually starts with only certain structures becoming identical. These are sets of sparse fractals that are rarely seen in the chaotic system.

Both systems have the same form of rare fractals. There must be a strong connection between the systems. The system's activity will cause dominant fractals to become the same. When describing the process, they called it the Zipper Effect, because it seems that as the system becomes stronger, it will gradually zip up more of the same.

The findings help us understand how self-organization can emerge from systems that don't have these properties. In cases that were never studied before, observing this process revealed new insights. Physicists study the change of parameters between chaotic systems. The group was able to expand the study of synchronization to extreme cases of chaotic systems that have a big difference between their parameters. It might be possible to shed light on how the brain works. Neural activity in the brain is chaotic. The brain's vast neural activity can be described using the stable fractal structures.

More information: Nir Lahav et al, Topological synchronization of chaotic systems, Scientific Reports (2022). DOI: 10.1038/s41598-022-06262-z Journal information: Scientific Reports Citation: Topological synchronization of chaotic systems (2022, April 22) retrieved 22 April 2022 from https://phys.org/news/2022-04-topological-synchronization-chaotic.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.