¿Podemos encontrar orden en el caos? Los físicos han demostrado, por primera vez, que los sistemas caóticos pueden sincronizarse debido a estructuras estables que emergen de la actividad caótica. Estas estructuras se conocen como fractales, formas con patrones que se repiten una y otra vez en diferentes escalas de la forma. A medida que se acoplan los sistemas caóticos, las estructuras fractales de los diferentes sistemas comenzarán a asimilarse entre sí, tomando la misma forma, haciendo que los sistemas se sincronicen.

Si los sistemas están fuertemente acoplados, las estructuras fractales de los dos sistemas eventualmente se volverán idénticas, provocando una sincronización completa entre los sistemas. Estos hallazgos nos ayudan a comprender cómo la sincronización y la autoorganización pueden surgir de sistemas que, para empezar, no tenían estas propiedades, como los sistemas caóticos y los sistemas biológicos.

Uno de los mayores desafíos de la física actual es comprender los sistemas caóticos. Caos, en física, tiene un significado muy específico. Los sistemas caóticos se comportan como sistemas aleatorios. Aunque siguen leyes deterministas, su dinámica aún cambiará erráticamente. Debido al conocido "efecto mariposa", su comportamiento futuro es impredecible (como el sistema meteorológico, por ejemplo).

Aunque los sistemas caóticos parecen aleatorios, no lo son, y podemos encontrar orden en el caos. De la actividad caótica surge una nueva estructura o patrón extraño conocido como atractor extraño. Si pasa suficiente tiempo, cada sistema caótico atraerá a su atractor extraño único y permanecerá en este patrón. Lo extraño de estos patrones es que están compuestos de fractales, estructuras con los mismos patrones que se repiten una y otra vez en diferentes escalas del fractal (muy parecido a la estructura ramificada de un árbol, por ejemplo). De hecho, los atractores extraños suelen estar compuestos por múltiples estructuras fractales. Diferentes conjuntos de estados del atractor extraño formarán parte de diferentes fractales y, aunque el sistema saltará erráticamente de un estado a otro, estos fractales se mantendrán estables a lo largo de la actividad caótica del sistema.

Debido al efecto mariposa, los sistemas caóticos parecen desafiar la sincronía. Their extreme erratic behavior suggests that two coupled chaotic systems cannot be synchronized and have the same activity. Yet, physicists discovered in the 80's that chaotic systems do synchronize. But how can that be?

A study by a group of physicists from Bar–Ilan University in Israel, recently published in the journal Scientific Reports , suggests a new answer to this puzzling question. According to the research, led by Dr. Nir Lahav, the emergence of the stable fractals is the key element that gives chaotic systems the ability to synchronize. They showed that as chaotic systems are being coupled, the fractal structures start to assimilate each other causing the systems to synchronize. If the systems are strongly coupled, the fractal structures of the two systems will eventually become identical, causing a complete synchronization between the systems. They termed this phenomenon Topological Synchronization. In low coupling, only small amounts of the fractal structures will become the same, and as the coupling between the systems grows, more fractal structures will become identical.

To their surprise, the physicists found that there is a specific trait for the process of how fractals from one system take similar form of the fractals from the other. They discovered that in completely different chaotic systems this process maintains the same form. When the two chaotic systems are weakly coupled, the process usually starts with only particular fractal structures becoming identical. These are sets of sparse fractals that rarely will emerge from the activity of the chaotic system.

Synchronization starts when these rare fractals take a similar form in both systems. To get complete synchronization there must be a strong coupling between the systems. Only then will dominant fractals, that emerge most of the time from the system's activity, also become the same. They called this process the Zipper Effect, because when describing it mathematically, it seems that as coupling between chaotic systems becomes stronger, it will gradually "zip up" more fractals to be the same.

These findings help us understand how synchronization and self-organization can emerge from systems that didn't have these properties to begin with. For example, observing this process revealed new insights about chaotic synchronization in cases that were never studied before. Usually, physicists study synchronization between similar chaotic systems with small change of parameters between them. Using topological synchronization, the group managed to expand the study of synchronization to extreme cases of chaotic systems that have a big difference between their parameters. Topological synchronization might even help us shed light on how neurons in the brain synchronize with each other. There is some evidence that neural activity in the brain is chaotic. If so, topological synchronization can describe how synchronization emerges from the vast neural activity of the brain using the stable fractal structures. + Explora más

Scientists reveal for first time the exact process by which chaotic systems synchronize