Article
Mathematics, Interdisciplinary Applications
Alejandro Carballosa, Alberto P. Munuzuri
Summary: This study proposes a mathematical model that analyzes the consequences of mixing on synchronization patterns. It finds that low levels of mixing can lead to irregular states and novel non-fully synchronized behaviors in a small parameter space.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
M. A. Ferre
Summary: Chimera states refer to a spatiotemporal phenomenon where coherence and incoherence dynamics coexist in homogeneous systems. Originally observed in non-locally coupled phase oscillators, this phenomenon has been observed in various systems including chaotic maps, time-delay systems, and complex networks. This review summarizes the different systems where chimera states are observed, focusing on theoretical and experimental contributions. It also critically examines the definitions of chimera states and presents some related works. Furthermore, new research perspectives are suggested due to the stage of the field.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Guillermo H. Goldsztein, Lars Q. English, Emma Behta, Hillel Finder, Alice N. Nadeau, Steven H. Strogatz
Summary: Using theory, experiment, and simulation, this study examines the dynamics of two coupled metronomes on a moving platform. The experiments show that the platform motion is damped by a dry friction force of Coulomb type, contrary to previous assumptions of viscous linear friction force. A new mathematical model is developed based on previous models but with a different treatment of friction. The model analysis reveals various long-term behaviors, including synchronization, phase locking, and suppression, shedding light on the dynamics of coupled metronomes.
Article
Physics, Fluids & Plasmas
Shuangjian Guo, Mingxue Yang, Wenchen Han, Junzhong Yang
Summary: Different types of dynamical states and their transitions were explored in a system composed of nonidentical phase oscillator subpopulations through numerical simulations and theoretical analyses. This study revealed the specific roles and relationships of chimera states in the system.
Article
Physics, Fluids & Plasmas
Biswabibek Bandyopadhyay, Tanmoy Banerjee
Summary: This study investigates the impact of Kerr anharmonicity on the symmetry-breaking phenomena of coupled quantum oscillators, revealing that Kerr nonlinearity hinders the process of symmetry breaking in both cases. The findings provide a means to control and engineer symmetry-breaking states for quantum technology.
Article
Multidisciplinary Sciences
Sindre W. Haugland, Anton Tosolini, Katharina Krischer
Summary: The text explores the behaviors of coupled oscillators, including synchronization and incoherence, as well as the discovery of "chimera states" and their relationship with synchronization and asynchronization. It demonstrates that globally coupled identical oscillators can express a wider range of coexistence patterns, including chimeras.
NATURE COMMUNICATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
E. V. Rybalova, A. Zakharova, G. I. Strelkova
Summary: In this study, we numerically investigated the spatiotemporal dynamics and synchronization of a heterogeneous two-layer multiplex network consisting of FitzHugh-Nagumo neurons. We found competitive behavior between solitary states and chimeras in the transition to synchronous regime with the introduction of interlayer coupling. By using different types of interlayer coupling, we systematically studied synchronization between different layers.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Anjuman Ara Khatun, Haider Hasan Jafri
Summary: The study explores the coexistence of synchronous and asynchronous dynamical behaviors in an ensemble of nonlinear oscillators coupled through different variables, resulting in chimera states. By tuning the coupling parameter in a different variable, the region of multistability can be shifted, providing an additional means to create chimera states. In an ensemble of coupled Rossler systems, multiple attractors and intertwined basins are observed, with the strength of incoherence (SI) serving as a useful order parameter for characterizing chimera states.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Hyunsuk Hong, Erik A. Martens
Summary: This study investigated the phase coherence dynamics in coupled oscillators based on the correlation between frequencies and coupling strengths. Results showed that in the case of correlated disorder, the oscillator population splits into two subpopulations, while in the uncorrelated case, it may split into four phase-locked subpopulations, leading to periodic global synchronization motion. In both cases of disorder, an incoherent state exists, with instability observed in the correlated case and neutral stability in the uncorrelated case.
Article
Physics, Fluids & Plasmas
Vyacheslav O. Munyayev, Maxim Bolotov, Lev A. Smirnov, Grigory Osipov, Igor Belykh
Summary: This study investigates the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and phase-lagged coupling. The findings show that the size of the coherent cluster and the coupling type have different effects on the stability of the solitary state.
Article
Physics, Multidisciplinary
Rico Berner, Simon Vock, Eckehard Schoell, Serhiy Yanchuk
Summary: The study developed a master stability approach for a wide class of adaptive networks, simplifying the synchronization problem to a low-dimensional system and revealing the interplay between adaptivity and network structure in the formation of stability islands and complex synchronization patterns.
PHYSICAL REVIEW LETTERS
(2021)
Article
Mathematics, Applied
N. D. Tsigkri-DeSmedt, N. Sarlis, A. Provata
Summary: Random links lead to the emergence of chimera-like states where coherent regions are interrupted by scattered, short-lived solitaries. Random links enhance the appearance of chimera-like states for values of the parameter space that otherwise support synchronization. This counter-intuitive effect is due to the system locally organizing into coherent and incoherent domains by adding random links to the synchronous state.
Article
Mathematics, Applied
Georgi S. Medvedev, Matthew S. Mizuhara, Andrew Phillips
Summary: In this study, we investigate a system of coupled phase oscillators driven by random intrinsic frequencies near a saddle-node on invariant circle bifurcation. The system undergoes a phase transition and changes its qualitative properties of collective dynamics under the variation of control parameters. By 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 demonstrate that heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before bifurcation and noncontractible ones after bifurcation. Both families are stable in the model at hand.
Article
Mathematics, Applied
Monica Goebel, Matthew S. Mizuhara, Sofia Stepanoff
Summary: Real-world systems of coupled oscillators can exhibit spontaneous synchronization and other complex behaviors. The interplay between network topology and emergent dynamics is a rich area of investigation. This study focuses on stability of twisted states in lattices of coupled Kuramoto oscillators, obtaining novel estimates and accurate numerical tests using the Jacobian matrix. The results have potential applications in higher dimensional systems beyond 2D square lattices.
Article
Mathematics, Applied
Zhen Su, Juergen Kurths, Yaru Liu, Serhiy Yanchuk
Summary: Extreme multistability refers to the appearance of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. In this study, we investigate a model of pendulum clocks coupled by springs and suspended on an oscillating base to demonstrate how extreme multistability can be induced through specifically designed coupling. Symmetric coupling is found to increase the dynamical complexity, leading to the generation of multiple isolated attractors and continuous families of stable periodic states. These coexisting states exhibit different levels of phase synchronization and can display splitting behavior.
Article
Mathematics, Applied
Zahra Dayani, Fatemeh Parastesh, Fahimeh Nazarimehr, Karthikeyan Rajagopal, Sajad Jafari, Eckehard Schoell, Juergen Kurths
Summary: In this paper, a time-varying coupling function is proposed to enhance synchronization in complex networks of oscillators. The stability of synchronization is analyzed using the master stability approach, considering the largest Lyapunov exponent of the linearized variational equations as the master stability function dependent on the network eigenvalues. Diffusive single-variable coupling is assumed for the oscillators, and the coupling with the smallest local Lyapunov exponent is selected for each time interval. The obtained coupling function decreases the critical coupling parameter, leading to enhanced synchronization. Moreover, it achieves faster synchronization and increased robustness. Illustratively, the optimal coupling function is found for three networks of chaotic Rossler, Chen, and Chua systems, showing enhanced synchronization.
Article
Mathematics, Applied
Max Thiele, Rico Berner, Peter A. A. Tass, Eckehard Schoell, Serhiy Yanchuk
Summary: This study presents a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. The phenomenon is manifested by temporal episodes of coherent and incoherent dynamics that alternate recurrently. Asymmetric adaptation rules and temporal separation between adaptation and individual node dynamics are identified as key features for the emergence of recurrent synchronization.
Article
Mathematics, Applied
Ralph G. Andrzejak, Anais Espinoso
Summary: Different synchronization types of chimera states have been discovered in multilayer networks. This study investigates the possible relationships between these synchronization types, specifically if the onset of one type implies the onset of another. Using a two-layer network with non-locally coupled phase oscillators, the researchers introduced mismatches in mean frequencies and phase lag parameters to make the layers non-identical. Various metrics were used to measure the degree of synchronization, including phase-locking, amplitude and phase synchronization between order parameters, generalized synchronization, and alignment of incoherent oscillator groups. Positive phase lag parameter mismatches resulted in a cascaded onset of synchronization, while negative mismatches led to most synchronization types occurring within a narrow range of coupling strength. Weaker couplings could destabilize chimera states in the response layer, and in the absence of a phase lag mismatch, sufficient coupling caused the response dynamics to replicate the driver dynamics with a constant phase lag.
Article
Mathematics, Applied
S. G. Ngueuteu Mbouna, Tanmoy Banerjee, Eckehard Schoell, Rene Yamapi
Summary: We investigate networks of coupled oscillators governed by fractional-order versions of van der Pol and Rayleigh oscillators and report the presence of diverse amplitude chimeras and oscillation death patterns. For the first time, amplitude chimeras are observed in a network of van der Pol oscillators. We also identify and characterize a form of amplitude chimera, called damped amplitude chimera, where the incoherent region(s) continuously increase in size over time and the oscillations of drifting units are continuously damped until they reach steady state. Decreasing the order of fractional derivatives increases the lifetime of classical amplitude chimeras and leads to a transition to damped amplitude chimeras. This study demonstrates that lower fractional derivatives reduce synchronization propensity and promote oscillation death phenomena that were not observed in networks of integer-order oscillators, such as solitary oscillation death and chimera death patterns.
Article
Clinical Neurology
Ralph G. G. Andrzejak, Hitten P. P. Zaveri, Andreas Schulze-Bonhage, Marc G. G. Leguia, William C. C. Stacey, Mark P. P. Richardson, Levin Kuhlmann, Klaus Lehnertz
Summary: Significant progress has been made recently in seizure forecasting. Wearable and implantable devices that record various signals have provided valuable data for analyzing seizure dynamics. Network science approaches have also contributed to understanding the pre-ictal dynamics of epileptic brains. A key challenge now is to effectively communicate the results of seizure-forecasting algorithms to patients, caretakers, and clinicians.
Article
Neurosciences
Riccardo Cusinato, Sigurd L. Alnes, Ellen van Maren, Ida Boccalaro, Debora Ledergerber, Antoine Adamantidis, Lukas L. Imbach, Kaspar Schindler, Maxime O. Baud, Athina Tzovara
Summary: During rest, intrinsic neural dynamics at multiple timescales increase in the auditory network, and exhibit spatial gradients in the neocortex. These intrinsic timescales can explain the latency of auditory responses, indicating their importance in auditory processing. This study provides insights into the repertoire of intrinsic neural dynamics in the human auditory system and their spatial organization.
JOURNAL OF NEUROSCIENCE
(2023)
Article
Physics, Multidisciplinary
Jan Fialkowski, Serhiy Yanchuk, Igor M. Sokolov, Eckehard Schoell, Georg A. Gottwald, Rico Berner
Summary: Phase transitions in equilibrium and nonequilibrium systems are important in the natural sciences. In dynamical networks, phase transitions organize changes in the collective behavior of coupled dynamical units. We demonstrate two distinct nonequilibrium phase transitions in a finite-size adaptive network, where the network's connectivity structure changes over time and coevolves with the nodes' dynamical state. Depending on the defects in the internal frequency distribution, we observe either an abrupt single-step transition or a more gradual multistep transition. This observation resembles heterogeneous nucleation.
PHYSICAL REVIEW LETTERS
(2023)
Article
Health Care Sciences & Services
Michael Single, Lena C. Bruhin, Narayan Schuetz, Aileen C. Naef, Heinz Hegi, Pascal Reuse, Kaspar A. Schindler, Paul Krack, Roland Wiest, Andrew Chan, Tobias Nef, Stephan M. Gerber
Summary: This paper presents the development of a novel sensor recording software system that supports the integration of heterogeneous sensor technologies and can reliably record longitudinal sensor measurements in research settings. Through qualitative and quantitative tests and evaluations, the feasibility and reliability of the software system were demonstrated. Conclusion: This software can be used to test sensor devices, develop and validate algorithms for extracting digital measures, and reduce barriers in sensor-enhanced biomedical research.
JMIR FORMATIVE RESEARCH
(2023)
Article
Clinical Neurology
Manuel Kostner, Michael Rebsamen, Piotr Radojewski, Christian Rummel, Baudouin Jin, Raphael Meier, Uzeyir Ahmadli, Kaspar Schindler, Roland Wiest
Summary: Prompt and accurate diagnosis is crucial in the management of epileptic seizures. This study evaluated the diagnostic value of visual analysis and automated quantification of perfusion MRI in distinguishing between ictal and postictal states in patients with seizures. The results showed that expert evaluation effectively differentiated between the two states, and the automated method correlated well with visual ratings.
BRAIN COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Elena Rybalova, Vasilii Nechaev, Eckehard Schoell, Galina Strelkova
Summary: This study numerically investigates the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The results show that the coupling strength range is the widest at the optimal noise level, and chimera states can be observed with a high probability.
Article
Mathematics, Applied
Ralph G. Andrzejak, Anais Espinoso, Eduardo Garcia-Portugues, Arthur Pewsey, Jacopo Epifanio, Marc G. Leguia, Kaspar Schindler
Summary: The article introduces how to quantify the concentration of unimodal circular data around the mean direction using the mean resultant length, and proposes a re-normalized version as an improvement. The relevance and effectiveness of the proposed method are illustrated through examples.
Article
Clinical Neurology
Michael Rebsamen, Baudouin Zongxin Jin, Tomas Klail, Sophie De Beukelaer, Rike Barth, Beata Rezny-Kasprzak, Uzeyir Ahmadli, Serge Vulliemoz, Margitta Seeck, Kaspar Schindler, Roland Wiest, Piotr Radojewski, Christian Rummel
Summary: The objective of this study was to assess the influence of quantitative reports (QReports) on the radiological assessment of hippocampal sclerosis (HS) from MRI of epilepsy patients in a clinical setting. The results showed that the accuracy of HS diagnosis and inter-rater agreement improved when using QReports. This study demonstrated the clinical feasibility and usefulness of QReports as an imaging biomarker for radiological assessment of HS.
CLINICAL NEURORADIOLOGY
(2023)
Article
Physics, Fluids & Plasmas
S. G. Ngueuteu Mbouna, Tanmoy Banerjee, Eckehard Schoell
Summary: In this paper, the study focuses on the investigation of symmetry-breaking phenomena in neuronal networks using simplified versions of the FitzHughNagumo model. The network of FitzHugh-Nagumo oscillators, in its original form, exhibits diverse partial synchronization patterns that are not observed in networks with simplified models. The study reports the discovery of a new type of chimera pattern and a peculiar hybrid state, as well as the emergence of oscillation death in the network. By deriving a reduced model, the transition from spatial chaos to oscillation death via the chimera state with a solitary state is explained. This study deepens the understanding of chimera patterns in neuronal networks.
Article
Physics, Fluids & Plasmas
Anais Espinoso, Ralph G. Andrzejak
Summary: The severe neurological disorder epilepsy affects almost 1% of the world population. This study introduces phase-based measures that can help detect features induced by epilepsy from EEG signals.
