Generalized synchronization in relay systems with instantaneous coupling

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Publication Details

Output type: Journal article

Author list: Gutierrez R, Sevilla-Escoboza R, Piedrahita P, Finke C, Feudel U, Buldu JM, Huerta-Cuellar G, Jaimes-Reategui R, Moreno Y, Boccaletti S

Publisher: American Physical Society

Publication year: 2013

Journal: Physical review E: Statistical, nonlinear, biological, and soft matter physics (1539-3755)

Volume number: 88

Issue number: 5

ISSN: 1539-3755

eISSN: 1550-2376

Languages: English-Great Britain (EN-GB)

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Open access status: green

Full text URL: https://oa.upm.es/31195/1/INVE_MEM_2013_176448.pdf

Abstract

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

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