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Sriram S, Mirzaei S, Mehrabbeik M, Rajagopal K, Rostami M, Jafari S. The influence of synaptic pathways on the synchronization patterns of regularly structured mChialvo map network. J Theor Biol 2023; 572:111591. [PMID: 37543300 DOI: 10.1016/j.jtbi.2023.111591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Revised: 07/26/2023] [Accepted: 07/28/2023] [Indexed: 08/07/2023]
Abstract
Synchronization of interconnecting units is one of the hottest topics many researchers are interested in. In addition, this emerging phenomenon is responsible for many biological processes, and thus, the synchronization of interacting neurons is an important field of study in neuroscience. Employing the memristive Chialvo (mChialvo) neuron map, this paper investigates the effect of electrical, inner-linking, chemical, and hybrid coupling functions on the synchronization state of a neuronal network with regular structure. Master stability function (MSF) analysis is performed to obtain the necessary conditions for synchronizing the built networks. Afterward, the MSF-based results are confirmed by calculating the synchronization error. Besides, the dynamics of the synchronous neurons are discussed based on the bifurcation analysis. Our results suggest that, compared to the electrical and inner-linking functions, chemical synapses facilitate mChialvo neurons' synchronization since the neurons can achieve synchrony with a negligible chemical coupling strength. Further studies reveal that based on the active synapses, coupled mChialvo neurons can reach cluster synchronization, chimera state, sine-like synchronization, phase synchronization, and cluster phase synchronization.
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Affiliation(s)
- Sridevi Sriram
- Centre for Computational Modelling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Simin Mirzaei
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Mehdi Rostami
- Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran; Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
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2
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Keane A, Neff A, Blaha K, Amann A, Hövel P. Transitional cluster dynamics in a model for delay-coupled chemical oscillators. CHAOS (WOODBURY, N.Y.) 2023; 33:2895974. [PMID: 37307156 DOI: 10.1063/5.0147645] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 05/15/2023] [Indexed: 06/14/2023]
Abstract
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in the experimental setup controls the onset of oscillations via a Hopf bifurcation. For a smaller voltage, the oscillators exhibit simple, so-called primary, clustering patterns, where all phase differences between each set of coupled oscillators are identical. However, upon increasing the voltage, secondary states, where phase differences differ, are detected, in addition to the primary states. Previous work on this system saw the development of a mathematical model that explained how the existence, stability, and common frequency of the experimentally observed cluster states could be accurately controlled by the delay time of the coupling. In this study, we revisit the mathematical model of the electrochemical oscillators in order to address open questions by means of bifurcation analysis. Our analysis reveals how the stable cluster states, corresponding to experimental observations, lose their stability via an assortment of bifurcation types. The analysis further reveals complex interconnectedness between branches of different cluster types. We find that each secondary state provides a continuous transition between certain primary states. These connections are explained by studying the phase space and parameter symmetries of the respective states. Furthermore, we show that it is only for a larger value of the voltage parameter that the branches of secondary states develop intervals of stability. For a smaller voltage, all the branches of secondary states are completely unstable and are, therefore, hidden to experimentalists.
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Affiliation(s)
- Andrew Keane
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
- Environmental Research Institute, University College Cork, Cork T23 XE10, Ireland
| | - Alannah Neff
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
| | - Karen Blaha
- Sandia National Labs, 1515 Eubank Blvd SE1515 Eubank Blvd SE, Albuquerque, New Mexico 87123, USA
| | - Andreas Amann
- School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland
| | - Philipp Hövel
- Department of Electrical and Information Engineering, Christian-Albrechts-Universität zu Kiel, Kaiserstr. 2, 24143 Kiel, Germany
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Iwamoto T, Sugitani Y, Masamura S, Konishi K, Hara N. Amplitude suppression of oscillators with delay connections and slow switching topology. Phys Rev E 2020; 102:032206. [PMID: 33076019 DOI: 10.1103/physreve.102.032206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 08/12/2020] [Indexed: 11/07/2022]
Abstract
The present paper shows that the amplitudes of oscillators in delay-coupled oscillator networks can be suppressed by switching the network topology at a rate much lower than the oscillator frequencies. The mechanism of suppression was clarified numerically, and a procedure for determining the connection parameters to induce suppression is presented. The analytical and numerical results were obtained with Stuart-Landau oscillators and were experimentally validated using double-scroll chaotic circuits.
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Affiliation(s)
- Tetsu Iwamoto
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
| | - Yoshiki Sugitani
- Department of Electrical and Electronic Systems Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan
| | - Shinnosuke Masamura
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
| | - Keiji Konishi
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
| | - Naoyuki Hara
- Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
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Blaha KA, Huang K, Della Rossa F, Pecora L, Hossein-Zadeh M, Sorrentino F. Cluster Synchronization in Multilayer Networks: A Fully Analog Experiment with LC Oscillators with Physically Dissimilar Coupling. PHYSICAL REVIEW LETTERS 2019; 122:014101. [PMID: 31012653 DOI: 10.1103/physrevlett.122.014101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2018] [Indexed: 06/09/2023]
Abstract
We investigate cluster synchronization in experiments with a multilayer network of electronic Colpitts oscillators, specifically a network with two interaction layers. We observe and analytically characterize the appearance of several cluster states as we change coupling in the layers. In this study, we innovatively combine bifurcation analysis and the computation of transverse Lyapunov exponents. We observe four kinds of synchronized states, from fully synchronous to a clustered quasiperiodic state-the first experimental observation of the latter state. Our work is the first to study fundamentally dissimilar kinds of coupling within an experimental multilayer network.
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Affiliation(s)
- Karen A Blaha
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Ke Huang
- Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Fabio Della Rossa
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
- Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Louis Pecora
- U.S. Naval Research Laboratory, Washington, DC 20375, USA
| | - Mani Hossein-Zadeh
- Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
- Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Chouzouris T, Omelchenko I, Zakharova A, Hlinka J, Jiruska P, Schöll E. Chimera states in brain networks: Empirical neural vs. modular fractal connectivity. CHAOS (WOODBURY, N.Y.) 2018; 28:045112. [PMID: 31906648 DOI: 10.1063/1.5009812] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.
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Affiliation(s)
- Teresa Chouzouris
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Iryna Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Jaroslav Hlinka
- Institute of Computer Science, Czech Academy of Sciences, Pod Vodarenskou vezi 2, 18207 Prague, Czech Republic
| | - Premysl Jiruska
- Institute of Physiology, Czech Academy of Sciences, Videnska 1083, 14220 Prague, Czech Republic
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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Kevrekidis YG, Kiss IZ, Kori H, Krischer K. Introduction to Focus Issue: In Memory of John L. Hudson: Self-Organized Structures in Chemical Systems. CHAOS (WOODBURY, N.Y.) 2018; 28:045001. [PMID: 31906653 DOI: 10.1063/1.5033452] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Affiliation(s)
- Yannis G Kevrekidis
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan
| | - Katharina Krischer
- Department of Physics, Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany
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Keane A, Krauskopf B, Postlethwaite CM. Climate models with delay differential equations. CHAOS (WOODBURY, N.Y.) 2017; 27:114309. [PMID: 29195317 DOI: 10.1063/1.5006923] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.
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Krishnagopal S, Lehnert J, Poel W, Zakharova A, Schöll E. Synchronization patterns: from network motifs to hierarchical networks. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160216. [PMID: 28115613 PMCID: PMC5311436 DOI: 10.1098/rsta.2016.0216] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/04/2016] [Indexed: 05/12/2023]
Abstract
We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analysing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridge the gap between mesoscale motifs and macroscopic networks.This article is part of the themed issue 'Horizons of cybernetical physics'.
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Affiliation(s)
- Sanjukta Krishnagopal
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
- Department of Physics, Birla Institute for Technology and Science Pilani, Pilani, Goa 403726, India
| | - Judith Lehnert
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Winnie Poel
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
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Nagao R, Zou W, Kurths J, Kiss IZ. Restoring oscillatory behavior from amplitude death with anti-phase synchronization patterns in networks of electrochemical oscillations. CHAOS (WOODBURY, N.Y.) 2016; 26:094808. [PMID: 27781452 DOI: 10.1063/1.4954040] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The dynamical behavior of delay-coupled networks of electrochemical reactions is investigated to explore the formation of amplitude death (AD) and the synchronization states in a parameter region around the amplitude death region. It is shown that difference coupling with odd and even numbered ring and random networks can produce the AD phenomenon. Furthermore, this AD can be restored by changing the coupling type from difference to direct coupling. The restored oscillations tend to create synchronization patterns in which neighboring elements are in nearly anti-phase configuration. The ring networks produce frozen and rotating phase waves, while the random network exhibits a complex synchronization pattern with interwoven frozen and propagating phase waves. The experimental results are interpreted with a coupled Stuart-Landau oscillator model. The experimental and theoretical results reveal that AD behavior is a robust feature of delayed coupled networks of chemical units; if an oscillatory behavior is required again, even a small amount of direct coupling could be sufficient to restore the oscillations. The restored nearly anti-phase oscillatory patterns, which, to a certain extent, reflect the symmetry of the network, represent an effective means to overcome the AD phenomenon.
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Affiliation(s)
- Raphael Nagao
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
| | - Wei Zou
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA
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Punetha N, Prasad A, Ramaswamy R. Phase-locked regimes in delay-coupled oscillator networks. CHAOS (WOODBURY, N.Y.) 2014; 24:043111. [PMID: 25554031 DOI: 10.1063/1.4897360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
For an ensemble of globally coupled oscillators with time-delayed interactions, an explicit relation for the frequency of synchronized dynamics corresponding to different phase behaviors is obtained. One class of solutions corresponds to globally synchronized in-phase oscillations. The other class of solutions have mixed phases, and these can be either randomly distributed or can be a splay state, namely with phases distributed uniformly on a circle. In the strong coupling limit and for larger networks, the in-phase synchronized configuration alone remains. Upon variation of the coupling strength or the size of the system, the frequency can change discontinuously, when there is a transition from one class of solutions to another. This can be from the in-phase state to a mixed-phase state, but can also occur between two in-phase configurations of different frequency. Analytical and numerical results are presented for coupled Landau-Stuart oscillators, while numerical results are shown for Rössler and FitzHugh-Nagumo systems.
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Affiliation(s)
- Nirmal Punetha
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
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Bell JG, Green JR, Wang J. Complex Reaction Dynamics in the Cerium–Bromate–2-Methyl-1,4-hydroquinone Photoreaction. J Phys Chem A 2014; 118:9795-800. [DOI: 10.1021/jp505378r] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jeffrey G. Bell
- Department of Chemistry and
Biochemistry, University of Windsor, Windsor, ON N9B 3P4, Canada
| | - James R. Green
- Department of Chemistry and
Biochemistry, University of Windsor, Windsor, ON N9B 3P4, Canada
| | - Jichang Wang
- Department of Chemistry and
Biochemistry, University of Windsor, Windsor, ON N9B 3P4, Canada
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Lehnert J, Hövel P, Selivanov A, Fradkov A, Schöll E. Controlling cluster synchronization by adapting the topology. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042914. [PMID: 25375574 DOI: 10.1103/physreve.90.042914] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2014] [Indexed: 06/04/2023]
Abstract
We suggest an adaptive control scheme for the control of in-phase and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized. It is robust towards different initial conditions as well as changes in the coupling parameters. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading to the stabilization of the desired cluster state. As a crucial parameter determining this interplay we identify the delay time. Furthermore, we show how to construct networks such that they exhibit not only a given cluster state but also with a given oscillation frequency. We apply our method to coupled Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in an expansion of systems close to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science.
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Affiliation(s)
- Judith Lehnert
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Philipp Hövel
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany and Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany
| | - Anton Selivanov
- Department of Theoretical Cybernetics, Saint-Petersburg State University, Saint-Petersburg, Russia
| | - Alexander Fradkov
- Department of Theoretical Cybernetics, Saint-Petersburg State University, Saint-Petersburg, Russia and Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoy Avenue, 61, Vasilievsky Ostrov, St. Petersburg, 199178 Russia
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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