1
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Vlachos I, Kugiumtzis D, Paluš M. Phase-based causality analysis with partial mutual information from mixed embedding. CHAOS (WOODBURY, N.Y.) 2022; 32:053111. [PMID: 35649985 DOI: 10.1063/5.0087910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.
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Affiliation(s)
- Ioannis Vlachos
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
| | - Dimitris Kugiumtzis
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
| | - Milan Paluš
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic
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2
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Moskalenko OI, Koronovskii AA, Selskii AO, Evstifeev EV. On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems. CHAOS (WOODBURY, N.Y.) 2021; 31:083106. [PMID: 34470237 DOI: 10.1063/5.0055302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
Multistability in the intermittent generalized synchronization regime in unidirectionally coupled chaotic systems has been found. To study such a phenomenon, the method for revealing the existence of multistable states in interacting systems being the modification of an auxiliary system approach has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled logistic maps and Rössler systems being in the intermittent generalized synchronization regime. The quantitative characteristic of multistability has been introduced into consideration.
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Affiliation(s)
- Olga I Moskalenko
- Physics of Open Systems Department, Institute of Physics, Saratov State University, 83, Astrakhanskaya, 410012 Saratov, Russia
| | - Alexey A Koronovskii
- Physics of Open Systems Department, Institute of Physics, Saratov State University, 83, Astrakhanskaya, 410012 Saratov, Russia
| | - Anton O Selskii
- Physics of Open Systems Department, Institute of Physics, Saratov State University, 83, Astrakhanskaya, 410012 Saratov, Russia
| | - Evgeniy V Evstifeev
- Physics of Open Systems Department, Institute of Physics, Saratov State University, 83, Astrakhanskaya, 410012 Saratov, Russia
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3
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Rakshit S, Ghosh D. Generalized synchronization on the onset of auxiliary system approach. CHAOS (WOODBURY, N.Y.) 2020; 30:111102. [PMID: 33261321 DOI: 10.1063/5.0030772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 10/12/2020] [Indexed: 06/12/2023]
Abstract
Generalized synchronization is an emergent functional relationship between the states of the interacting dynamical systems. To analyze the stability of a generalized synchronization state, the auxiliary system technique is a seminal approach that is broadly used nowadays. However, a few controversies have recently arisen concerning the applicability of this method. In this study, we systematically analyze the applicability of the auxiliary system approach for various coupling configurations. We analytically derive the auxiliary system approach for a drive-response coupling configuration from the definition of the generalized synchronization state. Numerically, we show that this technique is not always applicable for two bidirectionally coupled systems. Finally, we analytically derive the inapplicability of this approach for the network of coupled oscillators and also numerically verify it with an appropriate example.
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Affiliation(s)
- Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
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4
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Koronovskii AA, Moskalenko OI, Pivovarov AA, Evstifeev EV. Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators. CHAOS (WOODBURY, N.Y.) 2020; 30:083133. [PMID: 32872830 DOI: 10.1063/5.0007156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2020] [Accepted: 08/03/2020] [Indexed: 06/11/2023]
Abstract
The type of transition from asynchronous behavior to the generalized synchronization regime in mutually coupled chaotic oscillators has been studied. To separate the epochs of the synchronous and asynchronous motion in time series of mutually coupled chaotic oscillators, a method based on the local Lyapunov exponent calculation has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled dynamical systems for which the type of transition is well known. The transition to generalized synchronization regime in mutually coupled systems has been shown to be an on-off intermittency as well as in the case of the unidirectional coupling.
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Affiliation(s)
- Alexey A Koronovskii
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
| | - Olga I Moskalenko
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
| | - Anatoliy A Pivovarov
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
| | - Evgeniy V Evstifeev
- Faculty of Nonlinear Processes, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia
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Koronovskii AA, Moskalenko OI, Pivovarov AA, Khanadeev VA, Hramov AE, Pisarchik AN. Jump intermittency as a second type of transition to and from generalized synchronization. Phys Rev E 2020; 102:012205. [PMID: 32794947 DOI: 10.1103/physreve.102.012205] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 06/18/2020] [Indexed: 11/07/2022]
Abstract
The transition from asynchronous dynamics to generalized chaotic synchronization and then to completely synchronous dynamics is known to be accompanied by on-off intermittency. We show that there is another (second) type of the transition called jump intermittency which occurs near the boundary of generalized synchronization in chaotic systems with complex two-sheeted attractors. Although this transient behavior also exhibits intermittent dynamics, it differs sufficiently from on-off intermittency supposed hitherto to be the only type of motion corresponding to the transition to generalized synchronization. This type of transition has been revealed and the underling mechanism has been explained in both unidirectionally and mutually coupled chaotic Lorenz and Chen oscillators. To detect the epochs of synchronous and asynchronous motion in mutually coupled oscillators with complex topology of an attractor a technique based on finding time intervals when the phase trajectories are located on equal or different sheets of chaotic attractors of coupled oscillators has been developed. We have also shown that in the unidirectionally coupled systems the proposed technique gives the same results that may obtained with the help of the traditional method using the auxiliary system approach.
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Affiliation(s)
- Alexey A Koronovskii
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Olga I Moskalenko
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Anatolii A Pivovarov
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Vladislav A Khanadeev
- Saratov State University, 83 Astrakhanskaya Strasse, 410012 Saratov, Russia and Regional Scientific and Educational Mathematical Center "Mathematics of Future Technologies," 410012, Saratov, Russia
| | - Alexander E Hramov
- Innopolis University, 1 Universitetskaya Strasse, 420500 Innopolis, Russia
| | - Alexander N Pisarchik
- Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcón, Madrid, Spain
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6
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Lymburn T, Walker DM, Small M, Jüngling T. The reservoir's perspective on generalized synchronization. CHAOS (WOODBURY, N.Y.) 2019; 29:093133. [PMID: 31575144 DOI: 10.1063/1.5120733] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2019] [Accepted: 09/08/2019] [Indexed: 06/10/2023]
Abstract
We employ reservoir computing for a reconstruction task in coupled chaotic systems, across a range of dynamical relationships including generalized synchronization. For a drive-response setup, a temporal representation of the synchronized state is discussed as an alternative to the known instantaneous form. The reservoir has access to both representations through its fading memory property, each with advantages in different dynamical regimes. We also extract signatures of the maximal conditional Lyapunov exponent in the performance of variations of the reservoir topology. Moreover, the reservoir model reproduces different levels of consistency where there is no synchronization. In a bidirectional coupling setup, high reconstruction accuracy is achieved despite poor observability and independent of generalized synchronization.
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Affiliation(s)
- Thomas Lymburn
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - David M Walker
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Michael Small
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Thomas Jüngling
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
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7
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Frolov N, Maksimenko V, Lüttjohann A, Koronovskii A, Hramov A. Feed-forward artificial neural network provides data-driven inference of functional connectivity. CHAOS (WOODBURY, N.Y.) 2019; 29:091101. [PMID: 31575143 DOI: 10.1063/1.5117263] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2019] [Accepted: 08/10/2019] [Indexed: 06/10/2023]
Abstract
We propose a new model-free method based on the feed-forward artificial neuronal network for detecting functional connectivity in coupled systems. The developed method which does not require large computational costs and which is able to work with short data trials can be used for analysis and reconstruction of connectivity in experimental multichannel data of different nature. We test this approach on the chaotic Rössler system and demonstrate good agreement with the previous well-known results. Then, we use our method to predict functional connectivity thalamo-cortical network of epileptic brain based on ECoG data set of WAG/Rij rats with genetic predisposition to absence epilepsy. We show the emergence of functional interdependence between cortical layers and thalamic nuclei after epileptic discharge onset.
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Affiliation(s)
- Nikita Frolov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Vladimir Maksimenko
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Annika Lüttjohann
- Institute of Physiology I, University of Münster, Münster 48149, Germany
| | - Alexey Koronovskii
- Faculty of Nonlinear Processes, Saratov State University, 410012 Saratov, Russia
| | - Alexander Hramov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
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8
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Lymburn T, Khor A, Stemler T, Corrêa DC, Small M, Jüngling T. Consistency in echo-state networks. CHAOS (WOODBURY, N.Y.) 2019; 29:023118. [PMID: 30823707 DOI: 10.1063/1.5079686] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Accepted: 01/20/2019] [Indexed: 06/09/2023]
Abstract
Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test, we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.
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Affiliation(s)
- Thomas Lymburn
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Alexander Khor
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Thomas Stemler
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Débora C Corrêa
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Michael Small
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
| | - Thomas Jüngling
- Complex Systems Group, Department of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia
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9
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Sabarathinam S, Prasad A. Generalized synchronization in a conservative and nearly conservative systems of star network. CHAOS (WOODBURY, N.Y.) 2018; 28:113107. [PMID: 30501203 DOI: 10.1063/1.5030730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2018] [Accepted: 10/15/2018] [Indexed: 06/09/2023]
Abstract
We report the coexistence of synchronized and unsynchronized states in a mutually coupled star network of nearly conservative non-identical oscillators. Generalized synchronization is observed between the central oscillator with the peripherals, and phase synchronization is found among the peripherals in weakly dissipative systems. However, the basin size of the synchronization region decreases as dissipation strength is increased. We have demonstrated these phenomena with the help of Duffing and Lorenz84 oscillators with conservative, nearly conservative, and dissipative properties. The observed results are robust against the network size.
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Affiliation(s)
- S Sabarathinam
- Department of Physics and Astrophysics, University of Delhi, New Delhi 110007, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, New Delhi 110007, India
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10
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Jüngling T, Soriano MC, Oliver N, Porte X, Fischer I. Consistency properties of chaotic systems driven by time-delayed feedback. Phys Rev E 2018; 97:042202. [PMID: 29758606 DOI: 10.1103/physreve.97.042202] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Indexed: 06/08/2023]
Abstract
Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.
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Affiliation(s)
- T Jüngling
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - M C Soriano
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - N Oliver
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - X Porte
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - I Fischer
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
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11
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Malagarriga D, Villa AEP, Garcia-Ojalvo J, Pons AJ. Consistency of heterogeneous synchronization patterns in complex weighted networks. CHAOS (WOODBURY, N.Y.) 2017; 27:031102. [PMID: 28364768 DOI: 10.1063/1.4977972] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Synchronization within the dynamical nodes of a complex network is usually considered homogeneous through all the nodes. Here we show, in contrast, that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in small networks. We also analyze consistency, defined as the persistence of coexistent synchronization patterns regardless of the initial conditions. Our results show that complex weighted networks display richer consistency than regular networks, suggesting why certain functional network topologies are often constructed when experimental data are analyzed.
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Affiliation(s)
- D Malagarriga
- Departament de Física, Universitat Politècnica de Catalunya. Edifici Gaia, Rambla Sant Nebridi 22, 08222 Terrassa, Spain
| | - A E P Villa
- Neuroheuristic Research Group, Faculty of Business and Economics, University of Lausanne. CH-1015 Lausanne, Switzerland
| | - J Garcia-Ojalvo
- Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Dr. Aiguader 88, 08003 Barcelona, Spain
| | - A J Pons
- Departament de Física, Universitat Politècnica de Catalunya. Edifici Gaia, Rambla Sant Nebridi 22, 08222 Terrassa, Spain
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12
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Tandon A, Schröder M, Mannattil M, Timme M, Chakraborty S. Synchronizing noisy nonidentical oscillators by transient uncoupling. CHAOS (WOODBURY, N.Y.) 2016; 26:094817. [PMID: 27781477 DOI: 10.1063/1.4959141] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them-a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.
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Affiliation(s)
- Aditya Tandon
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
| | - Malte Schröder
- Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Manu Mannattil
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
| | - Marc Timme
- Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
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Malagarriga D, García-Vellisca MA, Villa AEP, Buldú JM, García-Ojalvo J, Pons AJ. Synchronization-based computation through networks of coupled oscillators. Front Comput Neurosci 2015; 9:97. [PMID: 26300765 PMCID: PMC4523791 DOI: 10.3389/fncom.2015.00097] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Accepted: 07/14/2015] [Indexed: 11/13/2022] Open
Abstract
The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.
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Affiliation(s)
- Daniel Malagarriga
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya Terrassa, Spain ; Neuroheuristic Research Group, HEC Lausanne, University of Lausanne Lausanne, Switzerland
| | - Mariano A García-Vellisca
- Laboratory of Biological Networks, Center for Biomedical Technology, Universidad Politécnica de Madrid Madrid, Spain
| | - Alessandro E P Villa
- Neuroheuristic Research Group, HEC Lausanne, University of Lausanne Lausanne, Switzerland
| | - Javier M Buldú
- Laboratory of Biological Networks, Center for Biomedical Technology, Universidad Politécnica de Madrid Madrid, Spain ; Complex Systems Group and GISC, Universidad Rey Juan Carlos Madrid, Spain
| | - Jordi García-Ojalvo
- Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park Barcelona, Spain
| | - Antonio J Pons
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya Terrassa, Spain
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14
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Liu S, Zhan M. Clustering versus non-clustering phase synchronizations. CHAOS (WOODBURY, N.Y.) 2014; 24:013104. [PMID: 24697366 DOI: 10.1063/1.4861685] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Clustering phase synchronization (CPS) is a common scenario to the global phase synchronization of coupled dynamical systems. In this work, a novel scenario, the non-clustering phase synchronization (NPS), is reported. It is found that coupled systems do not transit to the global synchronization until a certain sufficiently large coupling is attained, and there is no clustering prior to the global synchronization. To reveal the relationship between CPS and NPS, we further analyze the noise effect on coupled phase oscillators and find that the coupled oscillator system can change from CPS to NPS with the increase of noise intensity or system disorder. These findings are expected to shed light on the mechanism of various intriguing self-organized behaviors in coupled systems.
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Affiliation(s)
- Shuai Liu
- Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Meng Zhan
- Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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15
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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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Moskalenko OI, Koronovskii AA, Hramov AE. Inapplicability of an auxiliary-system approach to chaotic oscillators with mutual-type coupling and complex networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:064901. [PMID: 23848814 DOI: 10.1103/physreve.87.064901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2012] [Revised: 01/25/2013] [Indexed: 06/02/2023]
Abstract
The auxiliary system approach being de facto the standard for the study of generalized synchronization in the unidirectionally coupled chaotic oscillators is also widely used to examine the mutually coupled systems and networks of nonlinear elements with the complex topology of links between nodes. In this Brief Report we illustrate by two simple counterexamples that the auxiliary-system approach gives incorrect results for the mutually coupled oscillators and therefore to study the generalized synchronization this approach may be used only for the drive-response configuration of nonlinear oscillators and networks.
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Affiliation(s)
- Olga I Moskalenko
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.
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