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Sawicki J, Berner R, Loos SAM, Anvari M, Bader R, Barfuss W, Botta N, Brede N, Franović I, Gauthier DJ, Goldt S, Hajizadeh A, Hövel P, Karin O, Lorenz-Spreen P, Miehl C, Mölter J, Olmi S, Schöll E, Seif A, Tass PA, Volpe G, Yanchuk S, Kurths J. Perspectives on adaptive dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:071501. [PMID: 37486668 DOI: 10.1063/5.0147231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 05/24/2023] [Indexed: 07/25/2023]
Abstract
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Rico Berner
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Sarah A M Loos
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Mehrnaz Anvari
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Fraunhofer Institute for Algorithms and Scientific Computing, Schloss Birlinghoven, 53757 Sankt-Augustin, Germany
| | - Rolf Bader
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Wolfram Barfuss
- Transdisciplinary Research Area: Sustainable Futures, University of Bonn, 53113 Bonn, Germany
- Center for Development Research (ZEF), University of Bonn, 53113 Bonn, Germany
| | - Nicola Botta
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science and Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Nuria Brede
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science, University of Potsdam, An der Bahn 2, 14476 Potsdam, Germany
| | - Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Daniel J Gauthier
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Sebastian Goldt
- Department of Physics, International School of Advanced Studies (SISSA), Trieste, Italy
| | - Aida Hajizadeh
- Research Group Comparative Neuroscience, Leibniz Institute for Neurobiology, Magdeburg, Germany
| | - Philipp Hövel
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Omer Karin
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Philipp Lorenz-Spreen
- Center for Adaptive Rationality, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany
| | - Christoph Miehl
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Jan Mölter
- Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, Germany
| | - Simona Olmi
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Alireza Seif
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, California 94304, USA
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, Gothenburg, Sweden
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
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Zou W, Chen Y, Senthilkumar DV, Kurths J. Oscillation quenching in diffusively coupled dynamical networks with inertial effects. CHAOS (WOODBURY, N.Y.) 2022; 32:041102. [PMID: 35489855 DOI: 10.1063/5.0087839] [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: 03/22/2022] [Indexed: 06/14/2023]
Abstract
Self-sustained oscillations are ubiquitous and of fundamental importance for a variety of physical and biological systems including neural networks, cardiac dynamics, and circadian rhythms. In this work, oscillation quenching in diffusively coupled dynamical networks including "inertial" effects is analyzed. By adding inertia to diffusively coupled first-order oscillatory systems, we uncover that even small inertia is capable of eradicating the onset of oscillation quenching. We consolidate the generality of inertia in eradicating oscillation quenching by extensively examining diverse quenching scenarios, where macroscopic oscillations are extremely deteriorated and even completely lost in the corresponding models without inertia. The presence of inertia serves as an additional scheme to eradicate the onset of oscillation quenching, which does not need to tailor the coupling functions. Our findings imply that inertia of a system is an enabler against oscillation quenching in coupled dynamical networks, which, in turn, is helpful for understanding the emergence of rhythmic behaviors in complex coupled systems with amplitude degree of freedom.
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Affiliation(s)
- Wei Zou
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
| | - Yuxuan Chen
- School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
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Qian W, Papadopoulos L, Lu Z, Kroma-Wiley KA, Pasqualetti F, Bassett DS. Path-dependent dynamics induced by rewiring networks of inertial oscillators. Phys Rev E 2022; 105:024304. [PMID: 35291167 DOI: 10.1103/physreve.105.024304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 10/14/2021] [Indexed: 06/14/2023]
Abstract
In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when the network structure is time varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain may exhibit these properties simultaneously. It is thus relevant to ask how time-varying network connectivity impacts synchronization in systems that can exhibit multistability. To address this question, we study how the dynamics of coupled Kuramoto oscillators with inertia are affected when the topology of the underlying network changes in time. We show that hysteretic synchronization behavior in networks of coupled inertial oscillators can be driven by changes in connection topology alone. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony that remain even after the network returns to its initial configuration, and we show that these changes are robust to a wide range of network perturbations. Our findings highlight that the specific progression of network topology over time, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.
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Affiliation(s)
- William Qian
- Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Lia Papadopoulos
- Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zhixin Lu
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Keith A Kroma-Wiley
- Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Fabio Pasqualetti
- Department of Mechanical Engineering, University of California, Riverside, California 92521, USA
| | - Dani S Bassett
- Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- Department of Mechanical Engineering, University of California, Riverside, California 92521, USA
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- Santa Fe Institute, Santa Fe, New Mexico 87501, USA
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di Volo M, Segneri M, Goldobin DS, Politi A, Torcini A. Coherent oscillations in balanced neural networks driven by endogenous fluctuations. CHAOS (WOODBURY, N.Y.) 2022; 32:023120. [PMID: 35232059 DOI: 10.1063/5.0075751] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
We present a detailed analysis of the dynamical regimes observed in a balanced network of identical quadratic integrate-and-fire neurons with sparse connectivity for homogeneous and heterogeneous in-degree distributions. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean-field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self-consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean-field models upon tuning either the connectivity or the input DC current. In the heterogeneous situation, we analyze also the role of structural heterogeneity.
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Affiliation(s)
- Matteo di Volo
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, 95302 Cergy-Pontoise, France
| | - Marco Segneri
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, 95302 Cergy-Pontoise, France
| | - Denis S Goldobin
- Institute of Continuous Media Mechanics, Ural Branch of RAS, Acad. Korolev street 1, 614013 Perm, Russia
| | - Antonio Politi
- Institute for Pure and Applied Mathematics and Department of Physics (SUPA), Old Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - Alessandro Torcini
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, 95302 Cergy-Pontoise, France
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Gao J, Efstathiou K. Synchronized clusters in globally connected networks of second-order oscillators: Uncovering the role of inertia. CHAOS (WOODBURY, N.Y.) 2021; 31:093137. [PMID: 34598453 DOI: 10.1063/5.0057125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Accepted: 09/01/2021] [Indexed: 06/13/2023]
Abstract
We discuss the formation of secondary synchronized clusters, that is, small clusters of synchronized oscillators besides the main cluster, in second-order oscillator networks and the role of inertia in this process. Such secondary synchronized clusters give rise to non-stationary states such as oscillatory and standing wave states. After describing the formation of such clusters through numerical simulations, we use a time-periodic mean field ansatz to obtain a qualitative understanding of the formation of non-stationary states. Finally, the effect of inertia in the formation of secondary synchronized clusters is analyzed through a minimal model. The analysis shows that the effect of the main synchronized cluster on the other oscillators is weakened by inertias, thus leading to secondary synchronized clusters during the transition to synchronization.
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Affiliation(s)
- Jian Gao
- Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands
| | - Konstantinos Efstathiou
- Division of Natural and Applied Sciences and Zu Chongzhi Center for Mathematics and Computational Sciences, Duke Kunshan University, No. 8 Duke Avenue, Kunshan 215316, China
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Berner R, Yanchuk S, Schöll E. What adaptive neuronal networks teach us about power grids. Phys Rev E 2021; 103:042315. [PMID: 34005899 DOI: 10.1103/physreve.103.042315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the past decade. In this paper, we provide insight into the fundamental relation between these two types of networks. For this, we consider well-established models based on phase oscillators and show their intimate relation. In particular, we prove that phase oscillator models with inertia can be viewed as a particular class of adaptive networks. This relation holds even for more general classes of power grid models that include voltage dynamics. As an immediate consequence of this relation, we discover a plethora of multicluster states for phase oscillators with inertia. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.
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Affiliation(s)
- Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
| | - Serhiy Yanchuk
- Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, 10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
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Song H, Zhang X, Wu J, Qu Y. Low-frequency oscillations in coupled phase oscillators with inertia. Sci Rep 2019; 9:17414. [PMID: 31758069 PMCID: PMC6874549 DOI: 10.1038/s41598-019-53953-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2019] [Accepted: 09/30/2019] [Indexed: 11/26/2022] Open
Abstract
This work considers a second-order Kuramoto oscillator network periodically driven at one node to model low-frequency forced oscillations in power grids. The phase fluctuation magnitude at each node and the disturbance propagation in the network are numerically analyzed. The coupling strengths in this work are sufficiently large to ensure the stability of equilibria in the unforced system. It is found that the phase fluctuation is primarily determined by the network structural properties and forcing parameters, not the parameters specific to individual nodes such as power and damping. A new "resonance" phenomenon is observed in which the phase fluctuation magnitudes peak at certain critical coupling strength in the forced system. In the cases of long chain and ring-shaped networks, the Kuramoto model yields an important but somehow counter-intuitive result that the fluctuation magnitude distribution does not necessarily follow a simple attenuating trend along the propagation path and the fluctuation at nodes far from the disturbance source could be stronger than that at the source. These findings are relevant to low-frequency forced oscillations in power grids and will help advance the understanding of their dynamics and mechanisms and improve the detection and mitigation techniques.
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Affiliation(s)
- Huihui Song
- School of New energy, Harbin Institute of Technology-Weihai, Weihai, Shandong, 264209, China
| | - Xuewei Zhang
- College of Engineering, Texas A&M University-Kingsville, Kingsville, Texas, 78363, USA
| | - Jinjie Wu
- School of New energy, Harbin Institute of Technology-Weihai, Weihai, Shandong, 264209, China
| | - Yanbin Qu
- School of New energy, Harbin Institute of Technology-Weihai, Weihai, Shandong, 264209, China.
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Peron T, Messias F de Resende B, Mata AS, Rodrigues FA, Moreno Y. Onset of synchronization of Kuramoto oscillators in scale-free networks. Phys Rev E 2019; 100:042302. [PMID: 31770973 DOI: 10.1103/physreve.100.042302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 06/10/2023]
Abstract
Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent 2<γ≤3, in line with what has been observed for other dynamical processes in such networks. For γ>3, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.
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Affiliation(s)
- Thomas Peron
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, E-Zaragoza 50018, Spain
| | | | - Angélica S Mata
- Departamento de Física, Universidade Federal de Lavras, 37200-000 Lavras, Minas Gerais, Brazil
| | - Francisco A Rodrigues
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo 13566-590, Brazil
| | - Yamir Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, E-Zaragoza 50018, Spain
- Department of Theoretical Physics, University of Zaragoza, E-Zaragoza 50009, Spain
- ISI Foundation, I-10126 Torino, Italy
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Goldschmidt RJ, Pikovsky A, Politi A. Blinking chimeras in globally coupled rotators. CHAOS (WOODBURY, N.Y.) 2019; 29:071101. [PMID: 31370417 DOI: 10.1063/1.5105367] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2019] [Accepted: 06/10/2019] [Indexed: 06/10/2023]
Abstract
In globally coupled ensembles of identical oscillators so-called chimera states can be observed. The chimera state is a symmetry-broken regime, where a subset of oscillators forms a cluster, a synchronized population, while the rest of the system remains a collection of nonsynchronized, scattered units. We describe here a blinking chimera regime in an ensemble of seven globally coupled rotators (Kuramoto oscillators with inertia). It is characterized by a death-birth process, where a long-term stable cluster of four oscillators suddenly dissolves and is very quickly reborn with a new reshuffled configuration. We identify three different kinds of rare blinking events and give a quantitative characterization by applying stability analysis to the long-lived chaotic state and to the short-lived regular regimes that arise when the cluster dissolves.
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Affiliation(s)
| | - Arkady Pikovsky
- Department of Physics and Astronomy, University of Potsdam, Potsdam 10623, Germany
| | - Antonio Politi
- Institute of Pure and Applied Mathematics, University of Aberdeen, Aberdeen AB24 3FX, United Kingdom
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