Controlling chimera states in networks of phase oscillators

2018 edition

Giulia Ruzzene

Networks of oscillators are used to model a variety of natural and man-made complex systems. Synchronization phenomena are particularly relevant when studying the dynamical evolution of such models. Our research focuses on a fascinating discovery made by the Japanese physicist Kuramoto in 2002. He found that synchronization and desynchronization can coexist in the dynamics of a network of identical oscillators, so it is possible that the units that make up the network split spontaneously into two complementary groups, one characterised by synchronous behavior and one showing an erratic motion. This peculiar phenomenon was then named a chimera state by Abrams and Strogatz after the mythological creature hybrid of a goat, a lion and a snake, to underline the coexistence of entities that intuitively do not belong together. Chimera states have been studied in different model systems. Furthermore, analogies were drawn between chimera states and real-world phenomena, such as chemical oscillators, power grids and brain dynamics. We investigate how to control chimera states, that is how to provoke them for parameters for which they do not form spontaneously and how to control the position of one of the two groups. For phase oscillator networks, we show that chimeras can be controlled acting on the connectivity structure of the network and we investigate which is the minimal perturbation needed to achieve control. The simplicity of our control mechanism and the lack of direct manipulation of individual oscillators make it appealing for possible experimental applications.