New research from UC Davis and other universities explores the curious characteristics of networks.
Networks like the internet, powergrid and brain control our lives, yet the underlying dynamics that define them are somewhat mysterious. One of the most fascinating dynamics is the natural tendency for behavior in networks to synchronize.
A famous example of network synchronization occurs in groups of fireflies. Certain species will start blinking randomly and then adjust until thousands of them turn on and off at the same time. Besides synchronous behavior, scientists have also observed more complex repetitive patterns that can emerge between network nodes. They call these exotic states.
A more detailed study of these states might allow scientists to better create and decipher complex networks. Recently, researchers from UC Davis, Caltech and other universities made a significant contribution to this field. On Mar. 8th, they published a paper in Science describing what they learned from a new ideal system they created to study network dynamics.
The experimental system the researchers built is a ring of eight electrically connected nano-mechanical oscillators. Each oscillator can be thought of as a clock with only the minute hand. The figurative clocks can spin independently, but through some novel experimental design, electrical connections between them allow the oscillators to influence their neighbors in the ring. The system is essentially an ideal recreation of the firefly network. Each node, the firefly or oscillator, acts independently but can interact with the other nodes. When the connections in the system are switched on, the figurative clocks spin in an uncoordinated manner. Then, like the fireflies, they slowly lock into a stable state.
One of the states the research team found was perfect synchrony; all the figurative clocks turned identically. However, they saw other exotic states with more curious behavior. For example, they observed splay states where the figurative clocks moved at the same rate and direction, but each each clock was slightly offset from its nearest neighbors.
Each emergent state was based on the starting conditions of the oscillators. The experimenters turned on the system with hundreds of different initial conditions and observed as the exotic states emerged. Many of these states had been predicted theoretically but never recreated in an ideal experimental setting, others were observed for the first time.
According to Matt Matheny, a research scientist at Caltech who was the principal author on the study, the team combined the experimental data and mathematical theory to better characterize exotic states and begin to explain how and why they emerge.
“What we did is that we went through, and we explained why you get this sort of different behavior and showed mathematically that if you write out the equations you can pinpoint how these strange behaviors are stabilized.”
According to Michael Roukes, one of the leaders of the research and the Frank J. Roshek professor of physics, applied physics and bioengineering at Caltech, such precise analysis was possible in this experimental system because the researchers had full control over almost every aspect.
“This is a really well behaved system where we can both measure everything that’s going on and control everything in the system,” Roukes said. “Those are the ingredients that now give us this very robust and detailed experimental platform to sort through the various theories that have been proposed, put them to the test and expand them where they don’t explain what is manifested in the real world.”
Although the systems we deal with on a daily basis have more than 8 nodes and are connected in dramatically more complicated ways, the simplicity of the experimental system allowed the scientists to get a better understanding of the fundamentals of networks in a way that an observational study of complicated networks would never allow.
According to Raissa D’Souza, a professor of computer science and mechanical and aerospace engineering at UC Davis and another author on the paper, the team was pleasantly surprised by the sheer variety of exotic states that could emerge from a simple 8 node system. They were also daunted by what that could mean for more complicated real world networks.
“It’s the simplest kind of structure that we could think of, and already in that simple structure we see beautiful unanticipated patterns of coordinated behavior,” D’Souza said. “It’s a little staggering and exciting to think about what would happen if we start scaling up the complexity of the network beyond that ring.”
Yet scaling up the complexity of the network is exactly what the team plans to do next. They want to answer more questions about the fundamentals of synchrony and exotic states in more complicated systems.They’d like to see if it is possible to push the system between exotic states.
“One of the things that we really want to do is understand how we can nudge the system to go from one type of exotic state to a different type of exotic state,” D’Souza said. “We’d like to give it a small little push and take advantage of the natural dynamics of the system to push it from one behavior very simply to a different kind of behavior.”
This ability to nudge systems between states could potentially allow scientists to better control large scale networks and help manage issues in the human brain.
The researchers believe that one day, an understanding of exotic states may help make all sort of systems better.
Written by: Peter Smith – firstname.lastname@example.org