Exploiting the butterfly effect to control networks
Researchers at Northwestern University have come up with way to control increasingly complex networks by exploiting the way that these non-linear systems work. Networks composed out of millions of nodes react non-linearly to a disturbance, which essentially means that a small disturbance to a node could have a disproportionately large effect.
“A fundamental property of networks is that a perturbation to one node can affect other nodes, potentially causing the entire system to change behavior or fail,” says Adilson Motter, Professor of Physics at Northwestern University, who supervised the research. “We have turned this principle on its head for something positive: to control network behavior.”
The research could have a far-reaching effect on the modern ultra-connected world and find application in a wide range of different networks including, the internet, power grids, global air transportation, medical science and ecological networks.
“Previous research on network control has focused mainly on linear models, for the excellent reason that it is in principle much simpler to manipulate linear dynamics,” says lead author Sean Cornelius, a graduate student in Motter’s research group. “Real networks are nonlinear, however, which at first could be regarded as bad news but turns out to be a blessing in disguise. In the case of complex networks, ignoring nonlinearity would be like throwing out the baby with the bath water.”
Their approach is to take advantage of the fact that small interventions have a large effect on the whole networked system. So this means that they could use small controlled interventions to create a response over the entire network without needing to completely reprogram it. The key is finding these “control nodes” that have the largest effect on the network. “This can be one node out of tens, hundreds, or even thousands of nodes, depending on the application,” explains Motter.
Applications include treating a disease, where doctors can’t directly control the many thousands of genes in a cell, but hope to influence them all by manipulating a few key genes. Other areas they tested include power-grid networks where it is critical that power generators are synchronized. In case of weather disruption (such as a tree falling on a power line), they showed that by manipulating only few nodes, it was in principle possible to restore power-grid synchrony.
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