Can chaotic systems also synchronize with each other? Physicists from Bar-Ilan University in Israel, along with colleagues from Spain, India and Italy, analyzed the Rossler system and discovered new phenomena that have been overlooked until now.
For the first time the researchers were able to measure the fine grain process that leads from disorder to synchrony, discovering a new kind of synchronization between chaotic systems: Topological Synchronization. Traditionally, synchronization has been examined by comparing the time-course of activity of the two systems. Topological Synchronization instead examines synchronization by comparing the structures of the systems.
As per the researchers, “Every chaotic system attracts its own unique strange attractor. By Topological Synchronization we mean that two strange attractors have the same organization and structures. At the beginning of the synchronization process, small areas on one strange attractor have the same structure of the other attractor, meaning that they are already synced. At the end of the process, all the areas of one strange attractor will have the structure of the other and complete Topological Synchronization has been reached.”
This means that chaotic systems synchronize gradually through local structures that, surprisingly, kick off in the sparse areas of the system and only then spread to the more populated areas. In these sparse areas the activity is less chaotic than in other areas and, as a result, it is easier for these areas to sync relative to those that are much more erratic. (1)
In a fully chaotic system.
Small clearings of order.
And at the end, the system will be in sync.
In a totally ordered system.
Vast hidden oceans of chaos.
And at the beginning, the system will breed a new cosmos…
A new cosmos which will again be in order once more.
An order which will create a new chaos to engulf everything…
For the cosmos we live in is neither ordered nor chaotic.
The cosmos we live in just Is.
Trying to speak to us.
Trying to break its limitations and communicate.
Throw that stone into the calm lake.
Can you hear the roaring abyss?