Synchronizing chaos through a narrow slice of the spectrum

The idea that the whole can be found in each part of something has fascinated philosophers and scientists for a long time.

Electronic engineering strives to develop ever more specialized and efficient circuits exchanging signals that possess highly controlled characteristics. Across the most complex systems in nature, such as the brain, the generation of activity having features that present themselves similarly over different temporal scales is almost always observed.

Physicists and engineers have been investigating networks made of chaotic oscillators for decades in a quest to explore new and unconventional approaches to designing systems that can solve difficult computation and control problems. These are systems that are easy to realize with components.

Despite being simple in their structure, they can generate incredibly intricate and far from random behaviors.

The activity at each point in time is effectively unpredictable due to the extreme sensitivity of chaos. The distribution of frequencies and the geometry of the trajectory generated by chaotic signals are both stable and repeatable. The circuits are interesting as a basis for realizing new forms of distributed computation, for example, based on sensor readings, due to the fact that these circuits can change in many ways.

A recent study showed that they could be used to make neural network training simpler.

When two or more chaotic oscillators are coupled together, the most interesting behaviors emerge as they attract and repulse their activities while trying to find an equilibrium in ways that regular periodic oscillators can't. Two years ago, work done in our laboratory showed that these behaviors could be used to gather readings from distant sensors and provide statistics.

The complex nature of chaotic signals means that they feature broad frequencies, which are very different from those used in modern wireless communication. It becomes very difficult, if not impossible, to realizecouplings over the air. Mr. Boyan Li is the second author of the study.

There is a lot of literature about the effects of chaotic oscillators. A group of people coalescing together at a party, with unexpected remote inter-dependencies, reminds us of the binding problem in the brain.

Surprisingly, almost no studies have considered the possibility of using a mechanism to transfer only a small amount of frequencies. The researchers at Tokyo Tech decided to look at the behavior of the chaotic oscillators. They used a filter that they could tune to let through only a small amount of frequencies, while keeping a wired connection between them.

We decided to use a type of chaotic oscillator that is extremely simple and involves only one transistor and a few passive components. The family of oscillators was introduced about five years ago by researchers from Italy and Poland. The head of the unit where the study was conducted says that they became interested in understanding them.

Even without transferring the entire broad spectrum, the research team was able to demonstrate that it is possible to sync these oscillators, even though it is just a small portion of it. They like to think of this as a situation where the whole is found in a part.

The lower gigahertz region is close to where first- generation wireless devices work. The synchronization wasn't complete, which means that the oscillators didn't follow each other's activity.

The most interesting effects can be seen at the level of a network of nodes. One of our previous works showed that it is similar between the two things. Dr. Minati and Dr. Frasca co-discovered these circuits and later analyzed them together.

The researchers observed that while a narrow slice of the spectrum was enough to get some visible syncope, the center location and width of the filter had a bigger effect. They were able to see that the activity of the slave oscillator tracked the filter setting in different ways in different parts of the country.

This is a good example of the richness of behaviors that can be found in these circuits. The simpler responses of periodic systems are locked or not to each other. It is a long way from being able to realize effective applications using these phenomena, so this is fundamental research at the moment. "It's fascinating to think that in the future we may realize some aspects of sense using these unusual approaches," says the co-author of the study.

This type of research needs to be extended by understanding more deeply the phenomena and how they can be used to generate interesting collective activity. To meet all radio requirements and to substantially minimize the power consumption will be the two main engineering challenges.

If successful solutions are found to these challenges, then one of our main goals is to demonstrate usable distributed sensing in applications that are important to society, such as monitoring the condition of land in precision agriculture. All of the experimental recordings have been made freely available for use in future work after the methodology and results were reported in a recent article.

There are observations in single-transistor microwave oscillators and chaos. The article was published in the Journal of Chaos.