IITMM researchers discover new behaviour of large networks of coupled elements

Researchers at the Dynamical Chaos Laboratory of the UNN Institute of Information Technology, Mathematics and Mechanics (IITMM) have discovered a new, "cyclops" behaviour in large networks of coupled elements.

Many phenomena in our world, such as the interaction of neurons in the brain, can be described mathematically as interaction processes between coupled dynamical systems consisting of a large number of elements. When modelling such interactions to describe key scenarios, only the first order of coupling is usually considered due to the complexity of theoretical and numerical analysis.

The researchers of the Dynamical Chaos Laboratory at the IITMM Department of Control Theory and Systems: Vyacheslav Munyaev, Maxim Bolotov, Lev Smirnov, Grigory Osipov and Igor Belykh showed that when higher orders of interaction in the coupling are considered, an unexpected dynamical state, which they called the "cyclops" state, can arise in ensembles of coupled elements. Its structure is composed of two equally sized clusters  ("arms of Cyclops") symmetric about a solitary element ("the Cyclops’s eye"). In Greek mythology, the Cyclopes were one-eyed giants who were famed for their ability to build impressive structures.

The possibility for the existence of cyclops modes in models of large neuronal populations described by an ensemble of theta neurons has been demonstrated.

The work was published in the highly ranked journal Physical Review Letters (IF=9.161). V. O. Munyayev, M. I. Bolotov, L. A. Smirnov, G. V. Osipov, and I. Belykh. Cyclops States in Repulsive Kuramoto Networks: The Role of Higher-Order Coupling. Phys. Rev. Lett. 130, 107201 (2023)