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Scirè A, Annovazzi-Lodi V. The emergence of dynamic networks from many coupled polar oscillators: a paradigm for artificial life. Theory Biosci 2023; 142:291-299. [PMID: 37516712 DOI: 10.1007/s12064-023-00401-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 07/19/2023] [Indexed: 07/31/2023]
Abstract
This work concerns a many-body deterministic model that displays life-like properties such as emergence, complexity, self-organization, self-regulation, excitability and spontaneous compartmentalization. The model portraits the dynamics of an ensemble of locally coupled polar phase oscillators, moving in a two-dimensional space, that under certain conditions exhibit emergent superstructures. Those superstructures are self-organized dynamic networks, resulting from a synchronization process of many units, over length scales much greater than the interaction range. Such networks compartmentalize the two-dimensional space with no a priori constraints, due to the formation of porous transport walls, and represent a highly complex and novel non-linear behavior. The analysis is numerically carried out as a function of a control parameter showing distinct regimes: static pattern formation, dynamic excitable networks formation, intermittency and chaos. A statistical analysis is drawn to determine the control parameter ranges for the various behaviors to appear. The model and the results shown in this work are expected to contribute to the field of artificial life.
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Affiliation(s)
- Alessandro Scirè
- Dipartimento Di Ingegneria Industriale E Dell'Informazione, Università Di Pavia, 27100, Pavia, Italy.
| | - Valerio Annovazzi-Lodi
- Dipartimento Di Ingegneria Industriale E Dell'Informazione, Università Di Pavia, 27100, Pavia, Italy
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2
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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: 10] [Impact Index Per Article: 10.0] [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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Medvedev GS, Mizuhara MS, Phillips A. A global bifurcation organizing rhythmic activity in a coupled network. CHAOS (WOODBURY, N.Y.) 2022; 32:083116. [PMID: 36049909 DOI: 10.1063/5.0089946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
We study a system of coupled phase oscillators near a saddle-node on invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the qualitative properties of collective dynamics. Using Ott-Antonsen reduction and geometric techniques for ordinary differential equations, we identify heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we show that heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before bifurcation from noncontractibile ones after bifurcation. Both families are stable for the model at hand.
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Affiliation(s)
- Georgi S Medvedev
- Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Matthew S Mizuhara
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, New Jersey 08628, USA
| | - Andrew Phillips
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA
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Franović I, Eydam S, Yanchuk S, Berner R. Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:841829. [PMID: 36926089 PMCID: PMC10013072 DOI: 10.3389/fnetp.2022.841829] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 02/16/2022] [Indexed: 06/18/2023]
Abstract
We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.
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Affiliation(s)
- Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia
| | - Sebastian Eydam
- Neural Circuits and Computations Unit, RIKEN Center for Brain Science, Wako, Japan
| | - Serhiy Yanchuk
- Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
- Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Rico Berner
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
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Rybalova E, Strelkova G. Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps. CHAOS (WOODBURY, N.Y.) 2022; 32:021101. [PMID: 35232034 DOI: 10.1063/5.0082431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
We study numerically the impact of heterogeneity in parameters on the dynamics of nonlocally coupled discrete-time systems, which exhibit solitary states along the transition from coherence to incoherence. These partial synchronization patterns are described as states when single or several elements demonstrate different dynamics compared with the behavior of other elements in a network. Using as an example a ring network of nonlocally coupled Lozi maps, we explore the robustness of solitary states to heterogeneity in parameters of local dynamics or coupling strength. It is found that if these network parameters are continuously modulated by noise, solitary states are suppressed as the noise intensity increases. However, these states may persist in the case of static randomly distributed system parameters for a wide range of the distribution width. Domains of solitary state existence are constructed in the parameter plane of coupling strength and noise intensity using a cross-correlation coefficient.
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Affiliation(s)
- Elena Rybalova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Galina Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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6
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Klinshov VV, Kirillov SY, Nekorkin VI, Wolfrum M. Noise-induced dynamical regimes in a system of globally coupled excitable units. CHAOS (WOODBURY, N.Y.) 2021; 31:083103. [PMID: 34470239 DOI: 10.1063/5.0056504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 07/12/2021] [Indexed: 06/13/2023]
Abstract
We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear Fokker-Planck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size, this leads to additional dynamical features, such as collective excitability of different types and noise-induced switching and bursting. Moreover, we show how characteristic quantities such as macroscopic and microscopic variability of interspike intervals can depend in a non-monotonous way on the noise level.
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Affiliation(s)
- V V Klinshov
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
| | - S Yu Kirillov
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
| | - V I Nekorkin
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
| | - M Wolfrum
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
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Goldobin DS, di Volo M, Torcini A. Reduction Methodology for Fluctuation Driven Population Dynamics. PHYSICAL REVIEW LETTERS 2021; 127:038301. [PMID: 34328756 DOI: 10.1103/physrevlett.127.038301] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 03/24/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions due to the divergence of all the moments (cumulants). We have solved this problem by introducing a "pseudocumulants" expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsic and endogenous fluctuations, thus obtaining a unified mean-field formulation encompassing quenched and dynamical sources of disorder.
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Affiliation(s)
- Denis S Goldobin
- Institute of Continuous Media Mechanics, Ural Branch of RAS, Acad. Korolev Street 1, 614013 Perm, Russia
- Department of Theoretical Physics, Perm State University, Bukirev Street 15, 614990 Perm, Russia
| | - Matteo di Volo
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089, 95302 Cergy-Pontoise cedex, France
| | - Alessandro Torcini
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089, 95302 Cergy-Pontoise cedex, France
- CNR-Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- INFN Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, Florence, Italy
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Klinshov VV, Zlobin DA, Maryshev BS, Goldobin DS. Effect of noise on the collective dynamics of a heterogeneous population of active rotators. CHAOS (WOODBURY, N.Y.) 2021; 31:043101. [PMID: 34251241 DOI: 10.1063/5.0030266] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 03/22/2021] [Indexed: 06/13/2023]
Abstract
We study the collective dynamics of a heterogeneous population of globally coupled active rotators subject to intrinsic noise. The theory is constructed on the basis of the circular cumulant approach, which yields a low-dimensional model reduction for the macroscopic collective dynamics in the thermodynamic limit of an infinitely large population. With numerical simulation, we confirm a decent accuracy of the model reduction for a moderate noise strength; in particular, it correctly predicts the location of the bistability domains in the parameter space.
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Affiliation(s)
- V V Klinshov
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
| | - D A Zlobin
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
| | - B S Maryshev
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia
| | - D S Goldobin
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia
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Tyulkina IV, Goldobin DS, Klimenko LS, Poperechny IS, Raikher YL. Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott-Antonsen theory. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190259. [PMID: 32279627 PMCID: PMC7202769 DOI: 10.1098/rsta.2019.0259] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole-dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking Tb temperature is lower than that (Taf) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott-Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented. This article is part of the theme issue 'Patterns in soft and biological matters'.
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Affiliation(s)
- Irina V. Tyulkina
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia
| | - Denis S. Goldobin
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia
- Department of Theoretical Physics, Perm State University, Bukirev Street 15, Perm 614990, Russia
| | - Lyudmila S. Klimenko
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia
- Department of Theoretical Physics, Perm State University, Bukirev Street 15, Perm 614990, Russia
| | - Igor S. Poperechny
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia
| | - Yuriy L. Raikher
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, Perm 614068, Russia
- e-mail:
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