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Letellier C, Sendiña-Nadal I, Leyva I, Barbot JP. Generalized synchronization mediated by a flat coupling between structurally nonequivalent chaotic systems. CHAOS (WOODBURY, N.Y.) 2023; 33:093117. [PMID: 37703476 DOI: 10.1063/5.0156025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 08/14/2023] [Indexed: 09/15/2023]
Abstract
Synchronization of chaotic systems is usually investigated for structurally equivalent systems typically coupled through linear diffusive functions. Here, we focus on a particular type of coupling borrowed from a nonlinear control theory and based on the optimal placement of a sensor-a device measuring the chosen variable-and an actuator-a device applying the actuating (control) signal to a variable's derivative-in the response system, leading to the so-called flat control law. We aim to investigate the dynamics produced by a response system that is flat coupled to a drive system and to determine the degree of generalized synchronization between them using statistical and topological arguments. The general use of a flat control law for getting generalized synchronization is discussed.
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Affiliation(s)
- Christophe Letellier
- Rouen Normandie University-CORIA, Avenue de l'Université, F-76800 Saint-Etienne du Rouvray, France
| | - Irene Sendiña-Nadal
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - I Leyva
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - Jean-Pierre Barbot
- QUARTZ EA7393 Laboratory, ENSEA, 6 Avenue du Ponceau, 95014 Cergy-Pontoise, France
- LS2N, UMR 6004 CNRS, École Centrale de Nantes, 1 rue de la Noë, 44300 Nantes, France
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Gambuzza LV, Frasca M, Fortuna L, Boccaletti S. Inhomogeneity induces relay synchronization in complex networks. Phys Rev E 2016; 93:042203. [PMID: 27176289 DOI: 10.1103/physreve.93.042203] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2015] [Indexed: 11/07/2022]
Abstract
Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is demonstrated herein that relay synchronization is not limited to such simple motifs, rather it can emerge in larger and arbitrary network topologies. In particular, we show how this phenomenon can be observed in networks of chaotic systems in the presence of some mismatched units, the relay nodes, and how it is actually responsible for an enhancement of synchronization in the network.
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Affiliation(s)
| | - Mattia Frasca
- DIEEI, Università degli Studi di Catania, Catania, Italy
| | - Luigi Fortuna
- DIEEI, Università degli Studi di Catania, Catania, Italy
| | - Stefano Boccaletti
- CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.,The Embassy of Italy in Tel Aviv, 25 Hamered Street, 68125 Tel Aviv, Israel
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Gutiérrez R, Sevilla-Escoboza R, Piedrahita P, Finke C, Feudel U, Buldú JM, Huerta-Cuellar G, Jaimes-Reátegui R, Moreno Y, Boccaletti S. Generalized synchronization in relay systems with instantaneous coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052908. [PMID: 24329332 DOI: 10.1103/physreve.88.052908] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2013] [Revised: 09/23/2013] [Indexed: 06/03/2023]
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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Affiliation(s)
- R Gutiérrez
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - R Sevilla-Escoboza
- Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico and Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
| | - P Piedrahita
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain
| | - C Finke
- d-fine GmbH, Opernplatz 2, 60313 Frankfurt, Germany
| | - U Feudel
- ICBM, University of Oldenburg, Carl-von-Ossietzky-Strasse 9-11, 26111 Oldenburg, Germany and IPST, University of Maryland, College Park, Maryland 20742-2431, USA
| | - J M Buldú
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Technical University of Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain
| | - G Huerta-Cuellar
- Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico
| | - R Jaimes-Reátegui
- Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico
| | - Y Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain and Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain and Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin, Italy
| | - S Boccaletti
- CNR Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy
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