![]() This is good news for the brain avoiding epilepsy, as its highly modular structure brings a high proportion of convergent walks. So networks with many convergent walks are prone to poorer synchronisation. When those disturbances propagate through multiple neighbours and then converge on one person, that person is going to be much more likely to copy the out-of-sync moves than if only one of their neighbours was offbeat. These chains of potential disturbances are like walks on the network. In our dancing example, one person making the wrong steps might lead some neighbours astray, who may then lead some of their neighbours astray and so on. When more paired walks are convergent, disturbances tend to be reinforced. Image: Associate Professor Joseph Lizier, University of Sydney Pairs of walks on a network – of dancers here – can be convergent (left) when they reach the same endpoint, or divergent (right) when they reach different endpoints. The person might quickly recover by watching their friends, they might throw their friends off for a few steps before everyone recovers, or in the worst case it might just cause chaos. A disturbance might be one person starting to get some steps wrong. Strength of synchronisation means how well the sync can recover from disturbances. It can be useful to measure whether a system of oscillators can synchronise their actions, and how strong that synchronisation would be. An oscillator is something that periodically repeats the same pattern of activity, like the sequence of steps in a repetitive dance, and coupled oscillators are ones that can influence each other’s behaviour. Mathematicians can analyse sync by treating the individuals in the system as “ coupled oscillators”. We have also become interested in designing sync as a desired behaviour in human-made systems such as power grids (to keep them in phase). Scientists originally became interested in sync to understand the inner workings of natural systems. In new research published in Proceedings of the National Academy of Sciences, we show how the strength of synchronisation in a network depends on the structure of the connections between its members – whether they be brain cells, fireflies, or groups of dancers. How does this happen? What is it about a system that determines whether sync will emerge, and how strong it will be? ![]() Sync most often emerges spontaneously rather than through following the lead of some central timekeeper. Our heart cells all beat together (at least when things are going well), and synchronised electrical waves can help coordinate brain regions – but too much synchronisation of brain cells is what happens in an epileptic seizure. Synchronisation is important at a more basic level in our bodies, too. Fireflies too know the joy of synchronisation, timing their flashes together to create a larger display to attract mates. Getting in sync can be exhilarating when you’re dancing in rhythm with other people or clapping along in an audience.
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