Abstract
Chimera states are intriguing complex spatio-temporal patterns of coexisting coherent and incoherent domains. They can often be observed in networks with nonlocal coupling topology, where each element interacts with its neighbours within a fixed range. In small-size nonlocally 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 nonlocally 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 nonidentical 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 neighbouring layer.
Highlights
Networks of coupled oscillators are an intensively studied topic in non-linear science, they have a wide range of applications in physics, biology, chemistry, technology, and social sciences
We have demonstrated that the combination of the tweezer control for chimera states and multiplexing allows for successful stabilization of chimera states in both layers of two-layer networks of Van der Pol oscillators
Considering a ring topology with non-local interaction between the oscillators within each layer, and one-to-one connections between the corresponding oscillators from the two layers, we have focused on networks of relatively small size, where chimera states are usually hard to observe
Summary
Networks of coupled oscillators are an intensively studied topic in non-linear science, they have a wide range of applications in physics, biology, chemistry, technology, and social sciences. In small-size rings of non-locally coupled oscillators, chimera states are often short-living chaotic transients, which eventually collapse to the synchronized state. Chimera states exhibit a chaotic spatial motion of the position of the coherent and incoherent domains, which is more pronounced with decreasing of the system size [68] These two effects are weakly noticeable in large networks, but they strongly impede the observation of chimera states in small systems. We introduced a tweezer control scheme for stabilization of chimera states [76] in small-size non-locally coupled networks. In small networks of Van der Pol and FitzHugh-Nagumo oscillators, we demonstrated that tweezer control allows for stabilization of variable chimera patterns with different sizes of coherent domains [77]. We demonstrate that chimera states which are not observable in small isolated networks, can be efficiently stabilized by the combined action of multiplexing and tweezer control
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