Article
Physics, Fluids & Plasmas
Bojun Li, Nariya Uchida
Summary: The study shows that the multichimera state disappears when the phase delay parameter alpha exceeds a critical value, but reappears when further increased. A transition from multichimera to multitwisted states is observed, involving five collective phases.
Article
Physics, Fluids & Plasmas
Kazuha Itabashi, Quoc Hoan Tran, Yoshihiko Hasegawa
Summary: By proposing a topological approach to characterize the phase dynamics in coupled oscillators, this study gains insights into the collective dynamics of complex systems. The method extracts quantitative features describing the shape of the phase data and extends these features to time-variant characteristics. Combining these features with the kernel method allows for characterization of multiclustered synchronized dynamics and qualitative explanation of chimera states.
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
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
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
Physics, Multidisciplinary
Nikita P. Kryuchkov, Vladimir N. Mantsevich, Stanislav O. Yurchenko
Summary: This study numerically and analytically investigates the spectra of two harmonic oscillators with stochastically fluctuating coupling and driving forces, showing that the oscillation spectra exhibit mixing even at small coupling.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Rok Cestnik, Arkady Pikovsky
Summary: We study the collective behavior of phase oscillators in the thermodynamic limit and propose an Ansatz for the circular moments of the distribution that allows for truncation at any number of modes. By simulating a Josephson junction array, we demonstrate the higher-dimensional behavior facilitated by dynamics on extended manifolds.
PHYSICAL REVIEW LETTERS
(2022)
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
Nirmalendu Hui, Debabrata Biswas, Tanmoy Banerjee, Juergen Kurths
Summary: This paper discusses the effects of propagation delay in direct-indirect coupled oscillators, showing that even small delays can promote oscillatory behavior. Unlike in directly coupled oscillators, where delay induces amplitude death, here delay inhibits the death state and aids in the revival of oscillations. The study demonstrates that the dynamics of coupled oscillators are heavily influenced by the coupling function and the presence of time delay.
Article
Mathematics, Applied
David Mersing, Shannyn A. Tyler, Benjamas Ponboonjaroenchai, Mark R. Tinsley, Kenneth Showalter
Summary: The study investigates photochemically coupled micro-oscillators in star networks, showing that synchronization can be achieved through adjusting coupling strength. Both experimental and theoretical analysis provide insights into the synchronization mechanism, where phase divergence in heterogeneous oscillators can be realigned by perturbations from hub oscillator.
Article
Physics, Multidisciplinary
Rending Lu, Viet-Thanh Pham, Mo Chen, Quan Xu
Summary: The dynamics of coupled chaotic circuits, especially the Chua circuit, have been extensively studied in this paper. The formation of nonstationary chimera is observed in all coupling schemes. Only resistive coupling can achieve complete synchronization.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Mathematics, Applied
L. Messee Goulefack, Marlon F. Ramos, R. Yamapi, C. Anteneodo
Summary: In this study, the dynamics of nonlocally coupled Hindmarsh-Rose neurons modified by coupling the induced magnetic flux to the membrane potential with a quadratic memristor of strength k were investigated. The nonlocal coupling involved the interaction of each neuron with its neighbors within a fixed radius, influencing the membrane potential with coupling intensity sigma. The study examined how variations of k and sigma affect the collective dynamics, finding that coherence typically increased when k and sigma were increased, except for small parameter ranges where the opposite behavior could occur. Moreover, varying k also affected the pattern of bursts and spikes, resulting in an increase in burst frequency, a decrease in the number and amplitude of spikes, and longer quiescent periods.
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
Dawid Dudkowski, Krzysztof Czolczynski, Tomasz Kapitaniak
Summary: This paper introduces a novel type of chimera state, known as multi-headed loop chimera, by studying a network of pendulum clocks. The study examines the occurrence and stability of these chimera states, analyzing the geometrical regions of the system with the highest probability of their occurrence, discussing the mechanisms of their creation, and exploring the influence of global coupling on their stability. The paper also investigates the bifurcation analysis of these states and generalizes their appearance into large networks of oscillators.
Article
Computer Science, Artificial Intelligence
Felix Koester, Dominik Ehlert, Kathy Luedge
Summary: This paper analyzes the memory capacity of a delay-based reservoir computer using a Hopf normal form as nonlinearity, and calculates its linear as well as higher order recall capabilities. The results show that the total memory capacity is dependent on the ratio between the information input period and the time delay in the system.
COGNITIVE COMPUTATION
(2023)
Article
Physics, Multidisciplinary
Lina Jaurigue, Elizabeth Robertson, Janik Wolters, Kathy Luedge
Summary: Reservoir computing is a machine learning method that utilizes the response of a dynamical system to solve tasks, particularly suited for hardware implementation and effective in time series prediction tasks. While still requiring parameter optimization, including a time-delayed version of the input can improve performance significantly.
Editorial Material
Multidisciplinary Sciences
Lina Jaurigue, Kathy Luedge
Summary: Reservoir computing is a fast and low-cost training method suitable for various physical systems, which can accelerate the learning process. A new approach enables the hardware implementation of traditional machine learning algorithms in electronic and photonic systems.
NATURE COMMUNICATIONS
(2022)
Review
Materials Science, Multidisciplinary
Tobias Huelser, Felix Koester, Lina Jaurigue, Kathy Luedge
Summary: Delay-based reservoir computing has attracted attention in hardware implementation due to its relative simplicity. This review paper introduces the concept of delay-based reservoir computing without requiring a predetermined relationship between delay time and input clock cycle. By independently choosing delay times, an important degree of freedom is gained. The study discusses ways to enhance computing performance in reservoirs formed by delay-coupled oscillators and demonstrates the impact of delay time tuning.
OPTICAL MATERIALS EXPRESS
(2022)
Article
Multidisciplinary Sciences
Fabian Bohm, Diego Alonso-Urquijo, Guy Verschaffelt, Guy Van der Sande
Summary: Ising machines are a promising computational concept for neural network training and combinatorial optimization. However, their inefficiency in fast statistical sampling hinders their performance compared to digital computers. In this study, we introduce a universal concept of using noise injection to achieve ultrafast statistical sampling with analog Ising machines, enabling accurate sampling of Boltzmann distributions and unsupervised training of neural networks. Through simulations, it is found that Ising machines can perform statistical sampling orders-of-magnitudes faster than software-based methods, making them efficient tools for machine learning and other applications.
NATURE COMMUNICATIONS
(2022)
Article
Nanoscience & Nanotechnology
Tobias Huelser, Felix Koester, Kathy Luedge, Lina Jaurigue
Summary: This article investigates the relationship between information processing capacity and task performance, finding poor correlation between them. A new method for calculating task mean square error is proposed, and it is found that there is good consistency between predicted and actual errors as long as the task input sequences do not have long autocorrelation times.
Article
Optics
Leon Messner, Elizabeth Robertson, Luisa Esguerra, Kathy Luedge, Janik Wolters
Summary: The importance of researching multiplexed quantum memory systems for optical quantum computation and communication technologies is highlighted, as well as the current challenge of systems that only perform well with elaborate preparation. In this study, a multiplexed random-access memory is demonstrated to store up to four optical pulses using electromagnetically induced transparency in warm cesium vapor. The results show a mean internal storage efficiency of 36% and a 1/e lifetime of 3.2 microsecond, facilitating the implementation of multiplexed memories in future quantum communication and computation infrastructures.
Article
Physics, Applied
Stefan Meinecke, Kathy Luedge
Summary: In this study, using a delay-differential equation model, three distinct instabilities that limit the maximum achievable pump power for passively mode-locked semiconductor disk lasers were detected, understood, and classified, and linked to characteristic positive-net-gain windows. A simple analytic approximation was derived to quantitatively describe the stability boundary. The results enable the prediction of optimal laser-cavity configurations with respect to positive-net-gain instabilities and are of great relevance for the future development of passively mode-locked semiconductor disk lasers.
PHYSICAL REVIEW APPLIED
(2022)
Article
Mathematics, Applied
Felix Koester, Dhruvit Patel, Alexander Wikner, Lina Jaurigue, Kathy Luedge
Summary: We propose a new approach to dynamical system forecasting called data-informed-reservoir computing (DI-RC) that, while solely being based on data, yields increased accuracy, reduced computational cost, and mitigates tedious hyper-parameter optimization of the reservoir computer (RC).
Article
Physics, Applied
Andreas Thurn, Jochen Bissinger, Stefan Meinecke, Paul Schmiedeke, Sang Soon Oh, Weng W. Chow, Kathy Luedge, Gregor Koblmueller, Jonathan J. Finley
Summary: This study investigates the dynamics of GaAs-AlGaAs core-shell nanowire lasers at low temperatures and finds sustained intensity oscillations with frequencies ranging from 160 GHz to 260 GHz. These oscillations are attributed to the dynamic competition between photoinduced carrier heating and cooling via phonon scattering.
PHYSICAL REVIEW APPLIED
(2023)
Article
Materials Science, Multidisciplinary
Stefan Meinecke, Felix Koester, Dominik Christiansen, Kathy Luedge, Andreas Knorr, Malte Selig
Summary: We propose a data-driven approach to approximate nonlinear transient dynamics in solid-state systems efficiently. Our machine-learning model combines dimensionality reduction with a nonlinear vector autoregression scheme. We present outstanding time-series forecasting performance, along with an easy-to-deploy model and an inexpensive training routine.
Proceedings Paper
Computer Science, Artificial Intelligence
Lina C. Jaurigue, Elizabeth Robertson, Janik Wolters, Kathy Luedge
Summary: This article discusses the performance of photonic reservoir computing, focusing on the impact of delay lines and the interplay between coupling topology and performance for various benchmark tasks. The study shows that additional delayed input can be beneficial for reservoir computing setups, as it provides an easy tuning parameter to improve the performance on a range of tasks.
EMERGING TOPICS IN ARTIFICIAL INTELLIGENCE (ETAI) 2022
(2022)
Article
Computer Science, Artificial Intelligence
Felix Koester, Serhiy Yanchuk, Kathy Ludge
Summary: This study demonstrates that delay-based reservoir computers can be characterized by a universal master memory function (MMF) and provides linear memory capacity. An analytical description of the MMF is proposed for efficient computing and can be applied to various reservoir scenarios.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Optics
Jan Hausen, Bastian Herzog, Alexander Nelde, Stefan Meinecke, Nina Owschimikow, Kathy Luedge
Summary: The influence of optical feedback on semiconductor lasers is a widely studied field, recent research has shown that it is possible to induce periodic pulselike output by locking external cavity modes and relaxation oscillation frequency, particularly beneficial for quantum dot systems. The staircase behavior of oscillation frequency can be influenced by changing laser parameters, leading to regular pulselike oscillations through a reordering of Hopf bifurcations.
Article
Optics
Felix Koester, Serhiy Yanchuk, Kathy Ludge
Summary: This paper provides a deep insight into the computation capability of delay based reservoir computing through an eigenvalue analysis and finds a connection between task-independent memory capacity and the eigenvalue spectrum of the dynamical system. The performance of reservoir computing can be predicted by analyzing the small signal response of the reservoir. Analysis can be applied to any dynamical system used as a reservoir.
JOURNAL OF PHYSICS-PHOTONICS
(2021)
