Article
Mathematics, Applied
Zongkai Cai, Zhigang Zheng, Can Xu
Summary: This study investigates a variant of the Kuramoto model, revealing the existence of partial locking when introducing a power law function with exponent less than 1, and the absence of such phenomenon when the exponent is greater than or equal to 1. Through a specific assumption, the long-term macroscopic dynamics and corresponding critical properties of the model can be analytically described, while constructing a characteristic function to provide intuitive interpretation of the dynamic phenomena in the system.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
Summary: In this work, the authors analyze the Kuramoto model with inertia on a convergent family of graphs. They assume that the intrinsic frequencies of the oscillators are sampled from a probability distribution and that the network connectivity is assigned by a given graph. They study patterns that emerge when mixing loses stability under the variation of the coupling strength, identifying pitchfork and Andronov-Hopf bifurcations in the model with multimodal intrinsic frequency distributions.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Physics, Fluids & Plasmas
William Qian, Lia Papadopoulos, Zhixin Lu, Keith A. Kroma-Wiley, Fabio Pasqualetti, Dani S. Bassett
Summary: This study investigates the influence of interaction topology on synchronization in networks of coupled oscillators. It shows that changes in connection topology alone can drive hysteresis synchronization behavior in networks of coupled inertial oscillators. Certain fixed-density rewiring schemes induce significant changes to the level of global synchrony, which remain robust to network perturbations.
Article
Multidisciplinary Sciences
John Vandermeer, Zachary Hajian-Forooshani, Nicholas Medina, Ivette Perfecto
Summary: Ecological systems are complex and oscillatory, with the Kuramoto model being a popular analytical tool to study their structure. The model reveals synchrony groups corresponding to subnetworks of the natural system, with an overlying chimeric structure depending on inter-oscillator coupling strength. The Kuramoto model offers a novel perspective for exploring interesting questions about the structure of ecological systems.
ROYAL SOCIETY OPEN SCIENCE
(2021)
Article
Mathematics, Interdisciplinary Applications
M. S. Mahmoud, M. Medhat, Hilda A. Cerdeira, Hassan F. El-Nashar
Summary: We investigate a Kuramoto model with four nonidentical oscillators of different initial frequencies. When the coupling strength exceeds a threshold value, the oscillators fall into a fully phase locked state with a common frequency. By numerically determining the relevant parameters, we identify the distinct coupling constant that controls the transition to a complete frequency synchronization. We establish a specific phase condition and derive an analytical formula to calculate the coupling factor during the full phase locking state based on the initial frequencies of the oscillators.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Physics, Fluids & Plasmas
Nirmal Punetha, Lucas Wetzel
Summary: The production process of integrated electronic circuitry leads to heterogeneities on the component level, which affects the synchronization dynamics. Using a phase-model description, the study shows that heterogeneity can enhance the stability of synchronized states in networks of Kuramoto oscillators. This optimization of phase differences between clocks is not limited to electronic systems.
Article
Mathematics, Interdisciplinary Applications
Ana Elisa D. Barioni, Marcus A. M. de Aguiar
Summary: Studying the dynamics of coupled oscillator systems has wide applications in physics and biology. By extending the Kuramoto model and proposing an ansatz based on spherical harmonics decomposition, we simplified the complexity of the dynamic equations. Deriving the phase diagram of equilibrium solutions for different natural frequency distributions showed excellent agreement with numerical solutions of the full system dynamics.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physiology
Joe Rowland Adams, Aneta Stefanovska
Summary: Networks of oscillating processes are common in living systems, especially in the energy metabolism of individual cells. Introducing oscillating networks can increase the synchronization of models and help processes resist external disturbances. Compared to traditional models, models with fewer parameters and greater flexibility can produce oscillating outputs comparable to experimental measurements.
FRONTIERS IN PHYSIOLOGY
(2021)
Article
Mathematics
Anastasiia A. Emelianova, Vladimir I. Nekorkin
Summary: The study found that under the simplex interactions between network elements, mixed dynamics exhibit a high similarity between chaotic attractors and chaotic repellors, and the sum of Lyapunov exponents of the attractor and repeller is closer to zero. This indicates that the conservative properties of the system are more pronounced in the case of three elements compared to two.
Article
Mathematics
Dharma Raj Khatiwada
Summary: This paper investigates the synchronization of a finite number of oscillators in the presence of external perturbations. The results show that synchronization persists even under the influence of external factors, and occasional boosting of the coupling strength is enough to maintain the assembly of oscillators in a synchronized state persistently.
Article
Computer Science, Artificial Intelligence
Reza Farhangi, Mohammad Taghi Hamidi Beheshti
Summary: This paper investigates the synchronization of coupled Kuramoto oscillators and introduces necessary and sufficient conditions for frequency synchronization and phase cohesiveness. The key factors in network synchronization are found to be heterogeneity in network and phase shift in coupling function. Increasing the phase shift and oscillator heterogeneity complicates synchronization conditions.
NEURAL PROCESSING LETTERS
(2021)
Article
Physics, Fluids & Plasmas
Takehiro Ito, Keiji Konishi, Toru Sano, Hisaya Wakayama, Masatsugu Ogawa
Summary: An adaptive control law is proposed in this paper to achieve in-phase and antiphase synchronization in a pair of relaxation oscillators. The phase dynamics of the coupled oscillators is shown to be equivalent to Kuramoto phase oscillators, and the results are extended to networks with three or more oscillators. A systematic procedure for designing controller parameters for oscillator networks with all-to-all and ring topologies is also provided. Numerical simulations demonstrate the application of these analytical results in solving a dispatching problem encountered by automated guided vehicles (AGVs) in factories.
Article
Mathematics, Interdisciplinary Applications
A. A. Emelianova, V. I. Nekorkin
Summary: We investigated the impact of nonisochronism on mixed dynamics in a system of two adaptively coupled rotators and found that it can either induce or destroy mixed dynamics. The phenomenon was shown to be robust with a defined range of existence. Furthermore, we discovered an attractor-repeller bifurcation at the boundary of the parameter domain where mixed dynamics occurs, similar to a saddle-node bifurcation. We observed that the sum of the Lyapunov exponents of the chaotic attractor was lower for parameter values corresponding to mixed dynamics, and this lowest value coincided with the attractor-repeller bifurcation, indicating a stronger resemblance to a conservative system compared to the isochronous case. Additionally, we found that increasing the amplitude of the nonisochronous term reduced the Kantorovich-Rubinstein-Wasserstein distance between the attractor and the repeller, making them more alike and approaching a reversible core.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Moritz Thuemler, Xiaozhu Zhang, Marc Timme
Summary: The secure operation of electric power grids depends on their stability properties. For the third-order model, which captures voltage dynamics, three routes to instability have been established in the literature: pure rotor angle instability, pure voltage instability, and instability induced by the interplay of both. However, we demonstrate that one of these routes, pure voltage instability, is nonphysical as it requires infinite voltage amplitudes. We also show that voltage collapse dynamics can still occur in the absence of any voltage instabilities.
Article
Mathematics, Interdisciplinary Applications
Yong Lei, Xin-Jian Xu, Xiaofan Wang, Yong Zou, Juergen Kurths
Summary: The synchronization of oscillators is crucial for understanding the collective dynamics of various natural and artificial systems. In this study, we introduce a Lyapunov function that can be optimized to enhance synchrony of heterogeneous oscillators on sparse networks. We consider two optimization problems: frequency allocation and network design. Numerical experiments demonstrate that our proposed criterion outperforms existing methods, which can be explained by the correlation between node degree and frequency magnitude.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Carlo R. Laing
Article
Mathematical & Computational Biology
Carlo R. Laing
JOURNAL OF MATHEMATICAL NEUROSCIENCE
(2018)
Article
Biology
Karen McCulloch, Mick G. Roberts, Carlo R. Laing
MATHEMATICAL BIOSCIENCES
(2019)
Article
Computer Science, Cybernetics
Carlo R. Laing, Christian Blasche
BIOLOGICAL CYBERNETICS
(2020)
Article
Mathematics, Applied
Carlo R. Laing, Oleh Omel'chenko
Review
Mathematical & Computational Biology
Christian Bick, Marc Goodfellow, Carlo R. Laing, Erik A. Martens
JOURNAL OF MATHEMATICAL NEUROSCIENCE
(2020)
Article
Mathematics, Applied
Thomas N. Thiem, Felix P. Kemeth, Tom Bertalan, Carlo R. Laing, Ioannis G. Kevrekidis
Summary: This study introduces a data-driven coarse-graining methodology for discovering simplified models, including globally based models and locally based models.
Article
Mathematics, Applied
Carlo R. Laing
Summary: The study investigates a hybrid system that interpolates between a network supporting a "bump" pattern of theta neurons and a network supporting a "chimera" pattern of phase oscillators. Analysis reveals that in the limit of an infinite number of oscillators, the hybrid system exhibits a variety of states such as spatiotemporal chaos, traveling waves, and modulated traveling waves, with neither the bump nor chimera persisting over the entire range of parameters.
Article
Multidisciplinary Sciences
Oleh Omel'chenko, Carlo R. Laing
Summary: We analyze a continuum evolution equation for a ring network of theta neurons with non-local homogeneous coupling, providing an analytical description of all possible steady states and their stability. By considering various parameter sets, we identify the typical bifurcation scenarios of the network and establish a rigorous theoretical foundation for previously observed numerical results.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Mathematics, Applied
Carlo R. Laing
Summary: This paper investigates chimeras in networks of coupled oscillators. The Ott/Antonsen ansatz is used to obtain a continuum level description of the oscillators' dynamics. It is found that the stability of the solutions depends on the width of the domain, and different types of chimeras similar to those observed in one-dimensional and two-dimensional domains are identified.
Article
Multidisciplinary Sciences
Carlo R. Laing, Bernd Krauskopf
Summary: In this paper, we study a single theta neuron with delayed self-feedback and derive algebraic expressions for the existence and stability of periodic solutions in the presence of feedback. These periodic solutions are characterized by equally spaced pulses per delay interval, and the multistability increases with increasing delay time. This model provides an analytical basis for understanding pulsating dynamics in other excitable systems subject to delayed self-coupling.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Mathematics, Applied
Carlo R. R. Laing
Summary: Chimeras, characterized by coexisting synchronous and asynchronous oscillators, are observed in networks of coupled oscillators. In this study, we examine a network composed of N equal-sized populations positioned at equally spaced points on a ring. By employing the Ott/Antonsen ansatz, we derive coupled ordinary differential equations to describe the level of synchrony within each population and explain the phenomenon of chimeras using a self-consistency argument. We compare our results with existing knowledge for N = 2 and 3, and obtain new insights for populations ranging from 4 to 12, as well as make conjectures based on numerical evidence for larger numbers of populations. We observe macroscopic chaos for more than five populations, but suggest that this behavior diminishes with an increased number of populations.
Article
Physics, Fluids & Plasmas
Carlo R. Laing
Summary: This study investigates the existence and stability of chimeras (phenomenon where oscillators in one population synchronize while those in the other are asynchronous) in heterogeneous networks using mathematical models and methods. The results suggest that the stability of chimeras is disrupted when the heterogeneity of oscillators increases.
Article
Physics, Fluids & Plasmas
Carlo R. Laing
Summary: The study investigates the effects of varying the widths of the in- and out-degree distributions on the dynamics of networks of theta neurons. It is found that for synaptically coupled networks, the dynamics are independent of the out-degree distribution, while for gap junction coupled neurons, broadening the degree distribution varies the values of parameters at which there is an onset of collective oscillations.
Article
Physics, Fluids & Plasmas
Carlo R. Laing
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
