Article
Mathematics, Applied
Debora Amadori, Matteo Colangeli, Astrid Correa, Lamberto Rondoni
Summary: The dynamics of Kuramoto oscillators were investigated using the exact response theory based on the Dissipation Function. The Kuramoto dynamics undergoing synchronization transitions was analyzed and compared with the linear response theory, showing the failure of the latter and the success of the exact theory in handling systems undergoing phase transitions.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Interdisciplinary Applications
Julio D. da Fonseca, Edson D. Leonel, Rene O. Medrano-T
Summary: We derive a formula for the statistical distribution of instantaneous frequencies in the Kuramoto-Sakaguchi model. This is based on the Kuramoto-Sakaguchi's theory of globally coupled phase oscillators, where we provide a detailed review of its assumptions and the derivation process of its main results. Our formula, a stationary probability density function with a complex mathematical structure, aligns well with numerical simulations and provides insight into the stationary collective states of the Kuramoto-Sakaguchi model.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Mathematical
Georgi S. Medvedev, Mathew S. Mizuhara
Summary: This study analyzes the Kuramoto model of coupled phase oscillators with inertia on Erdos-Renyi graphs, identifying various two cluster patterns and studying their stability. The cluster dynamics are decomposed into two systems governing the macro dynamics of cluster centers of mass and the micro dynamics of individual oscillators in each cluster. Stability of the cluster dynamics depends on the stability of low-dimensional group motion and coherence of oscillators within each group.
JOURNAL OF STATISTICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Chenggui Yao, Fei Xu, Jianwei Shuai, Xiang Li
Summary: The environmental temperature plays a critical role in the propagation of firing rate in neural networks, with synchronization of firing rate being optimized at an appropriate temperature.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(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
Physics, Multidisciplinary
Jung-Wan Ryu, Alexandre Lazarescu, Rahul Marathe, Juzar Thingna
Summary: The study extends the standard Stuart-Landau dimer model by incorporating inertia and noise effects, and investigates its dynamics and stochastic thermodynamics. A new bistable phase emerges in the absence of noise at zero temperature, while thermodynamic observables exhibit bistability at finite temperatures.
NEW JOURNAL OF PHYSICS
(2021)
Article
Mathematics, Applied
Sridevi Sriram, Karthikeyan Rajagopal, Anitha Karthikeyan, Akif Akgul
Summary: The network connectivities are crucial for exhibiting diverse collective dynamics in complex systems. Hindmarsh-Rose neurons connected by electromagnetic interactions are used to demonstrate different dynamical states and transitions. Specifically, the dynamical behaviors of the system are explored under regular, small-world, and random network connectivities. The results show that increasing coupling intensity leads to a transition from desynchronization to traveling wave state for all considered network interactions. Furthermore, the investigation is extended to a three-layer multiplex network where synchronization is achieved in all layers with increasing coupling intensity, eventually reaching a rest state at high coupling strength.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Walter Bomela, Michael Sebek, Raphael Nagao, Bharat Singhal, Istvan Z. Kiss, Jr-Shin Li
Summary: The breakdown of spatiotemporal organization in networks can lead to diseases or large-scale malfunctions. To restore function, it is important to identify the optimal intervention site for re-stabilizing network behavior. By analyzing stability and identifying the most influential node, an optimal intervention strategy can be determined.
Article
Physics, Fluids & Plasmas
Lyle Muller, Jan Minac, Tung T. Nguyen
Summary: We studied the Kuramoto model with attractive sine coupling and introduced a complex-valued matrix formulation with an exact solution for analytical insight. The existence of a complex-valued form of the Kuramoto model demonstrates that reformulations in higher-order number fields may provide tractable analytical approaches in some cases.
Article
Mathematics, Applied
Xiang Ling, Wen-Bin Ju, Ning Guo, Kong-Jin Zhu, Chao-Yun Wu, Qing-Yi Hao
Summary: This study generalized the Kuramoto model to D dimensions using a complex network framework, and utilized the local synchronous order parameter between the agent and its neighbors as the controllable variable to adjust the coupling strength. The study found that the average connectivity and level of heterogeneity of networks affect the time-dependent, rhythmic, cyclic state.
Article
Mathematics, Applied
Georg Boerner, Fabio Schittler Neves, Marc Timme
Summary: Recent research has shown that symmetrically connected inhibitory neuron networks can perform basic computations and are resilient to system disruption. However, it is still unclear how to effectively adapt network parameters to perform robust computations. This study presents an analytical approach to derive such parameters and analyzes the dynamics of k-winners-takes-all computations.
Article
Multidisciplinary Sciences
Raphael Sarfati, Orit Peleg
Summary: Video recordings of fireflies reveal the presence of stable states with constant delays between different groups within a single swarm. These findings have implications for understanding the relationship between mathematical models and collective behavior.
Article
Physics, Multidisciplinary
Vedanta Thapar, Ram Ramaswamy
Summary: This study investigates the dynamics of a set of coupled nonlinear pendula suspended from a movable beam. The lengths of the pendula are random, resulting in a heterogeneous ensemble of coupled oscillators. When all the pendula have the same length, there are two possible synchronization patterns. However, when the lengths are random, the system dynamically separates into clusters or groups with similar dynamics.
INDIAN JOURNAL OF PHYSICS
(2023)
Article
Chemistry, Physical
Tsuyoshi Yamaguchi
Summary: Molecular dynamics simulation was used to study sound dispersion on the molecular scale in molecular liquids. The relationship between the longitudinal modulus and frequency was analyzed and compared with the frequency-dependent longitudinal modulus evaluated by the Kubo-Green theory. The findings showed that the sound dispersion in both monoatomic and polyatomic liquids can be explained by considering the viscoelasticity in the q = 0 limit.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Mathematics, Applied
Dongnam Ko, Seung-Yeal Ha, Euntaek Lee, Woojoo Shim
Summary: In this paper, recent progress on the emergent behaviors of stochastic particle models arising from collective dynamics is surveyed. The collective dynamics of interacting autonomous agents is commonly observed in nature and can be understood as a concentration formation in a state space. This topic has gained interest in the applied mathematics community due to its possible engineering applications and relation with nonlocal partial differential equations. The paper examines specific stochastic collective models, discusses the emergence of collective dynamics, and explores their applications in finance and optimization.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)