Solitary state in oscillatory system may help reveal more about neuronal networks

In London, the Millennium Bridge became an infamous example of a coupled oscillatory system when thousands of pedestrians inadvertently synchronous strides, causing the structure to sway. Understanding the dynamic states of oscillatory networks isn’t just relevant to engineers. The analysis of synchrony in systems can be useful to many scientific fields, including neuroscience.

Inspired by neuronal networks built from excitatory and inhibitory neurons, Teichmann et al. analyzed mixed oscillator networks consisting of attractive and repulsive connections, where attractive oscillators try to stay close to each other in phase and the repulsive oscillators try to stay far away from each other in phase. The researchers observed when they changed the strength of the repulsive connection, a solitary state – where a lone repulsive oscillator is far removed in phase space, and the rest are close together – emerged.

“This state is at the border between full synchrony, where both groups stay close together, and partial synchrony, where the oscillators in the repulsive group start to move independently of each other, and may explain the transition between these two,” said author Erik Teichmann.

The scientists used the Kuramoto-Sakaguchi model to analyze the transitions of their oscillator system. The model is mainly used for purely attractive or purely repulsive networks and rarely used to observe synchronization in mixed networks.

By using the model to learn more about mixed coupled oscillator systems, the researchers hope their findings can be applied to better understanding neuronal ensembles with excitatory and inhibitory connections.

“The solitary state, as we defined it, is just a very special, although interesting and surprising, state that may tell us something about the transition from full synchrony to partial synchronization,” said Teichmann.

Source: “Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions,” by Erik Teichmann and Michael Rosenblum, Chaos: An Interdisciplinary Journal of Nonlinear Science (2019). The article can be accessed at https://doi.org/10.1063/1.5118843 .