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Muolo R, Njougouo T, Gambuzza LV, Carletti T, Frasca M. Phase chimera states on nonlocal hyperrings. Phys Rev E 2024; 109:L022201. [PMID: 38491593 DOI: 10.1103/physreve.109.l022201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 01/08/2024] [Indexed: 03/18/2024]
Abstract
Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data, that complex systems are composed of multiple units experiencing many-body interactions that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a topology solely involving many-body, nonlocal, and nonregular interactions, hereby named nonlocal d-hyperring, (d+1) being the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and we show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are "flattened" to pairwise ones, the chimera behavior is weaker and more elusive.
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Affiliation(s)
- Riccardo Muolo
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Thierry Njougouo
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
- Faculty of Computer Science, University of Namur, B5000 Namur, Belgium
- Department of Electrical and Electronic Engineering, University of Buea, P.O. Box 63, Buea, Cameroon
| | - Lucia Valentina Gambuzza
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
| | - Timoteo Carletti
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Mattia Frasca
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
- Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", IASI-CNR, 00185 Roma, Italy
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2
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Medeiros ES, Omel'chenko O, Feudel U. Transient chimera states emerging from dynamical trapping in chaotic saddles. CHAOS (WOODBURY, N.Y.) 2023; 33:093130. [PMID: 37729099 DOI: 10.1063/5.0155857] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 08/30/2023] [Indexed: 09/22/2023]
Abstract
Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these systems, when networked with nonlocal coupling in a ring, are capable of forming chimera states, in which one subset of the units oscillates periodically in a synchronized state forming the coherent domain, while the complementary subset oscillates chaotically in the neighborhood of the chaotic saddle constituting the incoherent domain. We find two distinct transient chimera states distinguished by their abrupt or gradual termination. We analyze the lifetime of both chimera states, unraveling their dependence on coupling range and size. We find an optimal value for the coupling range yielding the longest lifetime for the chimera states. Moreover, we implement transversal stability analysis to demonstrate that the synchronized state is asymptotically stable for network configurations studied here.
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Affiliation(s)
- Everton S Medeiros
- Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, 26111 Oldenburg, Germany
| | - Oleh Omel'chenko
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
| | - Ulrike Feudel
- Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, 26111 Oldenburg, Germany
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3
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Ragavan A, Manoranjani M, Senthilkumar DV, Chandrasekar VK. Multistable chimera states in a smallest population of three coupled oscillators. Phys Rev E 2023; 107:044209. [PMID: 37198793 DOI: 10.1103/physreve.107.044209] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 03/28/2023] [Indexed: 05/19/2023]
Abstract
We uncover the emergence of distinct sets of multistable chimera states in addition to chimera death and synchronized states in a smallest population of three globally coupled oscillators with mean-field diffusive coupling. Sequence of torus bifurcations result in the manifestation of distinct periodic orbits as a function of the coupling strength, which in turn result in the genesis of distinct chimera states constituted by two synchronized oscillators coexisting with an asynchronous oscillator. Two subsequent Hopf bifurcations result in homogeneous and inhomogeneous steady states resulting in desynchronized steady states and chimera death state among the coupled oscillators. The periodic orbits and the steady states lose their stability via a sequence of saddle-loop and saddle-node bifurcations finally resulting in a stable synchronized state. We have generalized these results to N coupled oscillators and also deduced the variational equations corresponding to the perturbation transverse to the synchronization manifold and corroborated the synchronized state in the two-parameter phase diagrams using its largest eigenvalue. Chimera states in three coupled oscillators emerge as a solitary state in N coupled oscillator ensemble.
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Affiliation(s)
- A Ragavan
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - M Manoranjani
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - D V Senthilkumar
- School of Physics,Indian Institute of Science Education and Research, Thiruvananthapuram-695551, Kerala, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
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4
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Manoranjani M, Senthilkumar DV, Chandrasekar VK. Abrupt symmetry-preserving transition from the chimera state. Phys Rev E 2023; 107:034212. [PMID: 37072986 DOI: 10.1103/physreve.107.034212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2023] [Accepted: 03/09/2023] [Indexed: 04/20/2023]
Abstract
We consider two populations of the globally coupled Sakaguchi-Kuramoto model with the same intra- and interpopulations coupling strengths. The oscillators constituting the intrapopulation are identical whereas the interpopulations are nonidentical with a frequency mismatch. The asymmetry parameters ensure the permutation symmetry among the oscillators constituting the intrapopulation and a reflection symmetry among the oscillators constituting the interpopulation. We show that the chimera state manifests by spontaneously breaking the reflection symmetry and also exists in almost in the entire explored range of the asymmetry parameter without restricting to the near π/2 values of it. The saddle-node bifurcation mediates the abrupt transition from the symmetry breaking chimera state to the symmetry-preserving synchronized oscillatory state in the reverse trace, whereas the homoclinic bifurcation mediates the transition from the synchronized oscillatory state to synchronized steady state in the forward trace. We deduce the governing equations of motion for the macroscopic order parameters employing the finite-dimensional reduction by Watanabe and Strogatz. The analytical saddle-node and homoclinic bifurcation conditions agree well with the simulations results and the bifurcation curves.
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Affiliation(s)
- M Manoranjani
- Department of Physics, Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, India
| | - V K Chandrasekar
- Department of Physics,Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, India
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5
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Kaper TJ, Vo T. A new class of chimeras in locally coupled oscillators with small-amplitude, high-frequency asynchrony and large-amplitude, low-frequency synchrony. CHAOS (WOODBURY, N.Y.) 2021; 31:123111. [PMID: 34972325 DOI: 10.1063/5.0067421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 11/17/2021] [Indexed: 06/14/2023]
Abstract
Chimeras are surprising yet important states in which domains of decoherent (asynchronous) and coherent (synchronous) oscillations co-exist. In this article, we report on the discovery of a new class of chimeras, called mixed-amplitude chimera states, in which the structures, amplitudes, and frequencies of the oscillations differ substantially in the decoherent and coherent regions. These mixed-amplitude chimeras exhibit domains of decoherent small-amplitude oscillations (phase waves) coexisting with domains of stable and coherent large-amplitude or mixed-mode oscillations (MMOs). They are observed in a prototypical bistable partial differential equation with oscillatory dynamics, spatially homogeneous kinetics, and purely local, isotropic diffusion. They are observed in parameter regimes immediately adjacent to regimes in which common large-amplitude solutions exist, such as trigger waves, spatially homogeneous MMOs, and sharp-interface solutions. Also, key singularities, folded nodes, and folded saddles arising commonly in multi-scale, bistable systems play important roles, and these have not previously been studied in systems with chimeras. The discovery of these mixed-amplitude chimeras is an important advance for understanding some processes in neuroscience, pattern formation, and physics, which involve both small-amplitude and large-amplitude oscillations. It may also be of use for understanding some aspects of electroencephalogram recordings from animals that exhibit unihemispheric slow-wave sleep.
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Affiliation(s)
- Tasso J Kaper
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
| | - Theodore Vo
- School of Mathematics, Monash University, Clayton, Victoria 3800, Australia
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6
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Choe CU, Choe MH, Jang H, Kim RS. Symmetry breakings in two populations of oscillators coupled via diffusive environments: Chimera and heterosynchrony. Phys Rev E 2020; 101:042213. [PMID: 32422840 DOI: 10.1103/physreve.101.042213] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 03/16/2020] [Indexed: 11/07/2022]
Abstract
We consider two diffusively coupled populations of identical oscillators, where the oscillators in each population are coupled with a common dynamic environment. Existence and stability of a variety of stationary states are analyzed on the basis of the Ott-Antonsen reduction method, which reveals that the chimera state occurs under the diffusive coupling scheme. Furthermore, we find an exotic symmetry-breaking behavior, the so-called the heterosynchronous state, in which each population exhibits in-phase coherence, while the order parameters of two populations rotate at different phase velocities. The chimera and heterosynchronous states emerge from bistabilities of distinct states for decoupled population and occur as a unique continuation for weak diffusive couplings. The heterosynchronous state is caused by an indirect coupling scheme via dynamic environments and could occur for a finite-size system as well, even for the system that consists of one oscillator per population.
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Affiliation(s)
- Chol-Ung Choe
- Research Group for Nonlinear Dynamics, Department of Physics, University of Science, Unjong-District, Pyongyang, Democratic People's Republic of Korea
| | - Myong-Hui Choe
- Department of Mathematics, Pyongyang University of Railways, Hyongjesan-District, Pyongyang, Democratic People's Republic of Korea
| | - Hyok Jang
- Research Group for Nonlinear Dynamics, Department of Physics, University of Science, Unjong-District, Pyongyang, Democratic People's Republic of Korea
| | - Ryong-Son Kim
- Research Group for Nonlinear Dynamics, Department of Physics, University of Science, Unjong-District, Pyongyang, Democratic People's Republic of Korea
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7
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Clerc MG, Coulibaly S, Ferré MA, Tlidi M. Two-dimensional optical chimera states in an array of coupled waveguide resonators. CHAOS (WOODBURY, N.Y.) 2020; 30:043107. [PMID: 32357656 DOI: 10.1063/1.5133836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2019] [Accepted: 03/16/2020] [Indexed: 06/11/2023]
Abstract
Two-dimensional arrays of coupled waveguides or coupled microcavities allow us to confine and manipulate light. Based on a paradigmatic envelope equation, we show that these devices, subject to a coherent optical injection, support coexistence between a coherent and incoherent emission. In this regime, we show that two-dimensional chimera states can be generated. Depending on initial conditions, the system exhibits a family of two-dimensional chimera states and interaction between them. We characterize these two-dimensional structures by computing their Lyapunov spectrum and Yorke-Kaplan dimension. Finally, we show that two-dimensional chimera states are of spatiotemporal chaotic nature.
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Affiliation(s)
- M G Clerc
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - S Coulibaly
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - M A Ferré
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - M Tlidi
- Faculté des Sciences, Université Libre de Bruxelles (U.L.B), CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
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8
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Manoj K, Pawar SA, Dange S, Mondal S, Sujith RI, Surovyatkina E, Kurths J. Synchronization route to weak chimera in four candle-flame oscillators. Phys Rev E 2020; 100:062204. [PMID: 31962431 DOI: 10.1103/physreve.100.062204] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Indexed: 11/07/2022]
Abstract
Synchronization and chimera are examples of collective behavior observed in an ensemble of coupled nonlinear oscillators. Recent studies have focused on their discovery in systems with least possible number of oscillators. Here we present an experimental study revealing the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators. We further report the discovery of multiphase weak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera.
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Affiliation(s)
- Krishna Manoj
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Samadhan A Pawar
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Suraj Dange
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Sirshendu Mondal
- Department of Mechanical Engineering, National Institute of Technology Durgapur 713209, India
| | - R I Sujith
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Elena Surovyatkina
- Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.,Space Research Institute of Russian Academy of Sciences, Space Dynamics and Data Analysis Department, 117997 Moscow, Russian Federation
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.,Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany
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9
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Alvarez-Socorro AJ, Clerc MG, Ferré MA, Knobloch E. Front depinning by deterministic and stochastic fluctuations: A comparison. Phys Rev E 2019; 99:062226. [PMID: 31330663 DOI: 10.1103/physreve.99.062226] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Indexed: 11/07/2022]
Abstract
Driven dissipative many-body systems are described by differential equations for macroscopic variables which include fluctuations that account for ignored microscopic variables. Here, we investigate the effect of deterministic fluctuations, drawn from a system in a state of phase turbulence, on front dynamics. We show that despite these fluctuations a front may remain pinned, in contrast to fronts in systems with Gaussian white noise fluctuations, and explore the pinning-depinning transition. In the deterministic case, this transition is found to be robust but its location in parameter space is complex, generating a fractal-like structure. We describe this transition by deriving an equation for the front position, which takes the form of an overdamped system with a ratchet potential and chaotic forcing; this equation can, in turn, be transformed into a linear parametrically driven oscillator with a chaotically oscillating frequency. The resulting description provides an unambiguous characterization of the pinning-depinning transition in parameter space. A similar calculation for noise-driven front propagation shows that the pinning-depinning transition is washed out.
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Affiliation(s)
- A J Alvarez-Socorro
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - Marcel G Clerc
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - M A Ferré
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - Edgar Knobloch
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
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10
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A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter. ELECTRONICS 2019. [DOI: 10.3390/electronics8070756] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper presents a new method for evaluating the synchronization of quasi-periodic oscillations of two oscillators, termed “chimeric synchronization”. The family of metrics is proposed to create a neural network information converter based on a network of pulsed oscillators. In addition to transforming input information from digital to analogue, the converter can perform information processing after training the network by selecting control parameters. In the proposed neural network scheme, the data arrives at the input layer in the form of current levels of the oscillators and is converted into a set of non-repeating states of the chimeric synchronization of the output oscillator. By modelling a thermally coupled VO2-oscillator circuit, the network setup is demonstrated through the selection of coupling strength, power supply levels, and the synchronization efficiency parameter. The distribution of solutions depending on the operating mode of the oscillators, sub-threshold mode, or generation mode are revealed. Technological approaches for the implementation of a neural network information converter are proposed, and examples of its application for image filtering are demonstrated. The proposed method helps to significantly expand the capabilities of neuromorphic and logical devices based on synchronization effects.
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11
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Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices. ENTROPY 2019; 21:e21050523. [PMID: 33267237 PMCID: PMC7515012 DOI: 10.3390/e21050523] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Revised: 05/17/2019] [Accepted: 05/20/2019] [Indexed: 11/26/2022]
Abstract
Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states—the quiet state or the state of divergence. It appears that chimera states of spatiotemporal divergence do exist in the regions around the boundary lines separating these two steady states. It is demonstrated that digital image entropy can be used as an effective measure for the visualization of these regions of chimera states in different networks (regular, feed-forward, random, and small-world NCMM).
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12
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Cano AV, Cosenza MG. Asymmetric cluster and chimera dynamics in globally coupled systems. CHAOS (WOODBURY, N.Y.) 2018; 28:113119. [PMID: 30501202 DOI: 10.1063/1.5043398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Accepted: 11/06/2018] [Indexed: 06/09/2023]
Abstract
We investigate the emergence of chimera and cluster states possessing asymmetric dynamics in globally coupled systems, where the trajectories of oscillators belonging to different subpopulations exhibit different dynamical properties. In an asymmetric chimera state, the trajectory of an element in the synchronized subset is stationary or periodic, while that of an oscillator in the desynchronized subset is chaotic. In an asymmetric cluster state, the periods of the trajectories of elements belonging to different clusters are different. We consider a network of globally coupled chaotic maps as a simple model for the occurrence of such asymmetric states in spatiotemporal systems. We employ the analogy between a single map subject to a constant drive and the effective local dynamics in the globally coupled map system to elucidate the mechanisms for the emergence of asymmetric chimera and cluster states in the latter system. By obtaining the dynamical responses of the driven map, we establish a condition for the equivalence of the dynamics of the driven map and that of the system of globally coupled maps. This condition is applied to predict parameter values and subset partitions for the formation of asymmetric cluster and chimera states in the globally coupled system.
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Affiliation(s)
- A V Cano
- Grupo de Caos y Sistemas Complejos, Centro de Física Fundamental, Universidad de Los Andes, Mérida, Venezuela
| | - M G Cosenza
- Grupo de Caos y Sistemas Complejos, Centro de Física Fundamental, Universidad de Los Andes, Mérida, Venezuela
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13
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Clerc MG, Coulibaly S, Ferré MA, Rojas RG. Chimera states in a Duffing oscillators chain coupled to nearest neighbors. CHAOS (WOODBURY, N.Y.) 2018; 28:083126. [PMID: 30180634 DOI: 10.1063/1.5025038] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2018] [Accepted: 07/31/2018] [Indexed: 06/08/2023]
Abstract
Coupled nonlinear oscillators can present complex spatiotemporal behaviors. Here, we report the coexistence of coherent and incoherent domains, called chimera states, in an array of identical Duffing oscillators coupled to their nearest neighbors. The chimera states show a significant variation of amplitude in the desynchronized domain. These intriguing states are observed in the bistability region between a homogeneous state and a spatiotemporal chaotic one. These dynamical behaviors are characterized by their Lyapunov spectra and their global phase coherence order parameter. The local coupling between oscillators prevents one domain from invading the other one. Depending on initial conditions, a family of chimera states appear, organized in a snaking-like diagram.
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Affiliation(s)
- M G Clerc
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, 487-3 Santiago, Chile
| | - S Coulibaly
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - M A Ferré
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, 487-3 Santiago, Chile
| | - R G Rojas
- Intituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla, 4059 Valparaíso, Chile
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14
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Lazarides N, Tsironis GP. Multistable dissipative breathers and collective states in SQUID Lieb metamaterials. Phys Rev E 2018; 98:012207. [PMID: 30110756 DOI: 10.1103/physreve.98.012207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Indexed: 06/08/2023]
Abstract
A SQUID (Superconducting QUantum Interference Device) metamaterial on a Lieb lattice with nearest-neighbor coupling supports simultaneously stable dissipative breather families which are generated through a delicate balance of input power and intrinsic losses. Breather multistability is possible due to the peculiar snaking flux amplitude-frequency curve of single dissipative-driven SQUIDs, which for relatively high sinusoidal flux field amplitudes exhibits several stable and unstable solutions in a narrow frequency band around resonance. These breathers are very weakly interacting with each other, while multistability regimes with a different number of simultaneously stable breathers persist for substantial intervals of frequency, flux field amplitude, and coupling coefficients. Moreover, the emergence of chimera states as well as temporally chaotic states exhibiting spatial homogeneity within each sublattice of the Lieb lattice is demonstrated. The latter of the states emerge through an explosive hysteretic transition resembling explosive synchronization that has been reported before for various networks of oscillators.
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Affiliation(s)
- N Lazarides
- Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Greece
- National University of Science and Technology "MISiS," Leninsky Prospekt 4, Moscow 119049, Russia
| | - G P Tsironis
- Department of Physics, University of Crete, P. O. Box 2208, 71003 Heraklion, Greece
- National University of Science and Technology "MISiS," Leninsky Prospekt 4, Moscow 119049, Russia
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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15
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Premalatha K, Chandrasekar VK, Senthilvelan M, Lakshmanan M. Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators. CHAOS (WOODBURY, N.Y.) 2018; 28:033110. [PMID: 29604660 DOI: 10.1063/1.5006454] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera, and imperfect breathing chimera states in a locally coupled network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibits oscillations with large amplitudes, while the desynchronized group of oscillators oscillates with small amplitudes, and this behavior of coexistence of synchronized and desynchronized oscillations fluctuates with time. Then, we analyze the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely, the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyze the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We also find the stability of the transient and stable amplitude chimera states and traveling wave states for an appropriate number of oscillators using Floquet theory. In addition, we also find the stability of the incoherent oscillation death states.
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Affiliation(s)
- K Premalatha
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India
| | - V K Chandrasekar
- Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401, Tamil Nadu, India
| | - M Senthilvelan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India
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16
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Nicolaou ZG, Riecke H, Motter AE. Chimera States in Continuous Media: Existence and Distinctness. PHYSICAL REVIEW LETTERS 2017; 119:244101. [PMID: 29286751 DOI: 10.1103/physrevlett.119.244101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2017] [Indexed: 06/07/2023]
Abstract
The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises the question of whether an analogous phenomenon can occur in continuous media. Here, we show that chimera states can exist in continuous systems even when the coupling is strictly local, as in many fluid and pattern forming media. Using the complex Ginzburg-Landau equation as a model system, we characterize chimera states consisting of a coherent domain of a frozen spiral structure and an incoherent domain of amplitude turbulence. We show that in this case, in contrast with discrete network systems, fluctuations in the local coupling field play a crucial role in limiting the coherent regions. We suggest these findings shed light on new possible forms of coexisting order and disorder in fluid systems.
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Affiliation(s)
- Zachary G Nicolaou
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Hermann Riecke
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA
| | - Adilson E Motter
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA
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Petrungaro G, Uriu K, Morelli LG. Mobility-induced persistent chimera states. Phys Rev E 2017; 96:062210. [PMID: 29347445 DOI: 10.1103/physreve.96.062210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2017] [Indexed: 06/07/2023]
Abstract
We study the dynamics of mobile, locally coupled identical oscillators in the presence of coupling delays. We find different kinds of chimera states in which coherent in-phase and antiphase domains coexist with incoherent domains. These chimera states are dynamic and can persist for long times for intermediate mobility values. We discuss the mechanisms leading to the formation of these chimera states in different mobility regimes. This finding could be relevant for natural and technological systems composed of mobile communicating agents.
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Affiliation(s)
- Gabriela Petrungaro
- Instituto de Investigación en Biomedicina de Buenos Aires (IBioBA)-CONICET-Partner Institute of the Max Planck Society, Polo Científico Tecnológico, Godoy Cruz 2390, Buenos Aires C1425FQD, Argentina
- Departamento de Física, FCEyN UBA, Ciudad Universitaria, Buenos Aires 1428, Argentina
| | - Koichiro Uriu
- Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan
| | - Luis G Morelli
- Instituto de Investigación en Biomedicina de Buenos Aires (IBioBA)-CONICET-Partner Institute of the Max Planck Society, Polo Científico Tecnológico, Godoy Cruz 2390, Buenos Aires C1425FQD, Argentina
- Departamento de Física, FCEyN UBA, Ciudad Universitaria, Buenos Aires 1428, Argentina
- Max Planck Institute for Molecular Physiology, Department of Systemic Cell Biology, Otto-Hahn-Strasse 11, Dortmund D-44227, Germany
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Clerc MG, Ferré MA, Coulibaly S, Rojas RG, Tlidi M. Chimera-like states in an array of coupled-waveguide resonators. OPTICS LETTERS 2017; 42:2906-2909. [PMID: 28957204 DOI: 10.1364/ol.42.002906] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Accepted: 06/29/2017] [Indexed: 06/07/2023]
Abstract
We consider coupled-waveguide resonators subject to optical injection. The dynamics of this simple device are described by the discrete Lugiato-Lefever equation. We show that chimera-like states can be stabilized, thanks to the discrete nature of the coupled-waveguide resonators. Such chaotic localized structures are unstable in the continuous Lugiato-Lefever model; this is because of dispersive radiation from the tails of localized structures in the form of two counter-propagating fronts between the homogeneous and the complex spatiotemporal state. We characterize the formation of chimera-like states by computing the Lyapunov spectra. We show that localized states have an intermittent spatiotemporal chaotic dynamical nature. These states are generated in a parameter regime characterized by a coexistence between a uniform steady state and a spatiotemporal intermittency state.
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Liu Z, Ouali M, Coulibaly S, Clerc MG, Taki M, Tlidi M. Characterization of spatiotemporal chaos in a Kerr optical frequency comb and in all fiber cavities. OPTICS LETTERS 2017; 42:1063-1066. [PMID: 28295092 DOI: 10.1364/ol.42.001063] [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
Complex spatiotemporal dynamics have been a subject of recent experimental investigations in optical frequency comb microresonators and in driven fiber cavities with Kerr-type media. We show that this complex behavior has a spatiotemporal chaotic nature. We determine numerically the Lyapunov spectra, allowing us to characterize different dynamical behavior occurring in these simple devices. The Yorke-Kaplan dimension is used as an order parameter to characterize the bifurcation diagram. We identify a wide regime of parameters where the system exhibits a coexistence between the spatiotemporal chaos, the oscillatory localized structure, and the homogeneous steady state. The destabilization of an oscillatory localized state through radiation of counter-propagating fronts between the homogeneous and the spatiotemporal chaotic states is analyzed. To characterize better the spatiotemporal chaos, we estimate the front speed as a function of the pump intensity.
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Cano AV, Cosenza MG. Chimeras and clusters in networks of hyperbolic chaotic oscillators. Phys Rev E 2017; 95:030202. [PMID: 28415379 DOI: 10.1103/physreve.95.030202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2017] [Indexed: 06/07/2023]
Abstract
We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.
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Affiliation(s)
- A V Cano
- Grupo de Caos y Sistemas Complejos, Centro de Física Fundamental, Universidad de Los Andes, Mérida 5101, Mérida, Venezuela
| | - M G Cosenza
- Grupo de Caos y Sistemas Complejos, Centro de Física Fundamental, Universidad de Los Andes, Mérida 5101, Mérida, Venezuela
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Kouvaris NE, Requejo RJ, Hizanidis J, Díaz-Guilera A. Chimera states in a network-organized public goods game with destructive agents. CHAOS (WOODBURY, N.Y.) 2016; 26:123108. [PMID: 28039967 DOI: 10.1063/1.4971974] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We found that a network-organized metapopulation of cooperators, defectors, and destructive agents playing the public goods game with mutations can collectively reach global synchronization or chimera states. Global synchronization is accompanied by a collective periodic burst of cooperation, whereas chimera states reflect the tendency of the networked metapopulation to be fragmented in clusters of synchronous and incoherent bursts of cooperation. Numerical simulations have shown that the system's dynamics switches between these two steady states through a first order transition. Depending on the parameters determining the dynamical and topological properties, chimera states with different numbers of coherent and incoherent clusters are observed. Our results present the first systematic study of chimera states and their characterization in the context of evolutionary game theory. This provides a valuable insight into the details of their occurrence, extending the relevance of such states to natural and social systems.
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Affiliation(s)
- Nikos E Kouvaris
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Rubén J Requejo
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Johanne Hizanidis
- Crete Center for Quantum Complexity and Nanotechnology, Physics Department, University of Crete, 71003 Heraklion, Greece
| | - Albert Díaz-Guilera
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
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