Disorder can make complex networks more stable and robust
Mathematics researchers show that complex systems, like power grids and the brain, may be stabilized by disorder among their constituent components
Researchers funded by the U.S. National Science Foundation have developed a mathematical framework that identifies when disorder in a system can actually make the system more stable. The research team found that many complex systems comprised of lots of parts (like generators in a power grid or neurons in a brain) can become more stable when their parts, or the interactions among them, are different.
Rather than treating such variations as flaws, the findings suggest scientists and engineers could deliberately use disorder to build more robust power grids, materials and other complex and interconnected systems. The work could also help explain why disorder is so prevalent in natural networks, including neural, biological and ecological systems. The results were published in the journal Science and supported by the NSF Applied Mathematics program and the NSF-Simons National Institute for Theory and Mathematics in Biology.
From flocks of birds to power grids to materials, interconnected systems depend on their ability to withstand disturbances. A gust of wind can scatter a flock, a sudden surge in demand can disrupt a power grid, and an impact can break a material. Scientists study these systems as networks comprised of individual components, or nodes, connected by links. In a power grid, for example, generators are the nodes and transmission lines represent the links.
Previous studies suggested that variations in such networks could be beneficial for their stability. To examine how complex and realistic network dynamics affect stability, the researchers mathematically analyzed systems near a stable state. Then, they calculated whether small disturbances faded away — allowing the system to return to its stable state — or grew, pushing the system toward instability. Finally, the team compared networks comprising identical components to networks with varying components and connections.
Their resulting framework can help scientists and engineers pinpoint the level of disorder that helps a system achieve optimal stability. The work could help improve the design of new systems, such as custom-made materials. Such materials typically are made of repeated, identical building blocks. Deliberately varying those blocks' shapes, sizes, orientations, and physical properties could enable useful new properties for a broad range of applications.
The researchers also developed a website that allows users to visualize how the framework works. By changing various parameters, users can watch the components in a system interact, synchronize, and organize into patterns.
This article was originally published by Northwestern University. It has been edited for length and style.
Read the full story: Networks could benefit from more disorder