Control of Chimera States in Multilayer Networks

Abstract

Chimera states are intriguing complex spatio-temporal patterns of coexisting coherent and incoherent domains. They can often be observed in networks with non-local coupling topology, where each element interacts with its neighbors within a fixed range. In small-size non-locally coupled networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the incoherent domain. This problem can be solved with a tweezer feedback control which can stabilize and fix the position of chimera states. We analyse the action of the tweezer control in two-layer networks, where each layer is a small non-locally coupled ring of Van der Pol oscillators. We demonstrate that tweezer control, applied to only one layer, successfully stabilizes chimera patterns in the other, uncontrolled layer, even in the case of non-identical layers. These results might be useful for applications in multilayer networks, where one of the layers cannot be directly accessed, thus it can be effectively controlled via a neighboring layer.