Article
Mathematics, Interdisciplinary Applications
Amit Sharma
Summary: This study reports the emergence of explosive synchronization in ensembles of non-identical coupled oscillators using attractive and repulsive mean-field coupling. The role of repulsive mean-field coupling is essential in inducing a first-order transition from incoherent to coherent states, depending on the strength of the coupling and distribution of intrinsic oscillator parameters. The existence of explosive synchronization is numerically studied in the parameter plane using order parameters for limit-cycle oscillators with symmetric and asymmetric distributions in the intrinsic oscillator parameters.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
I. A. Shepelev, S. S. Muni, T. E. Vadivasova
Summary: In a 2D lattice of self-sustained oscillators interacting nonlocally through an active nonlinear element, various spatiotemporal patterns emerge, including standing waves with periodic dynamics and complex cluster structures such as chimera states. The variation of coupling parameters leads to different spatiotemporal patterns, with some new periodic states arising from the repulsive part of the coupling. The influence of coupling nonlinearity on spatiotemporal dynamics is also demonstrated.
Article
Mathematics, Interdisciplinary Applications
Xuan Wang, Zhigang Zheng, Can Xu
Summary: The attractive and repulsive adaptive coupling schemes among dynamical agents have attracted increasing interest in systems ranging from physics to neuroscience. By extending the classical Kuramoto model, we propose a particular adaptive scheme for globally coupled phase oscillators, which captures the explosive synchronization induced by adaptive interactions. Our simulations reveal the transitions of overall weights and correlations between microscopic structure features and local dynamics as triggers for explosive synchronization, providing insights into the formation of small synchronized clusters. We also provide an analytical treatment for the reduced system, enhancing the understanding of abrupt dynamic phenomena in networked oscillators with generic adaptive schemes.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Igor A. Shepelev, Sishu S. Muni, Eckehard Schoell, Galina I. Strelkova
Summary: In a bilayer network of van der Pol oscillators with repulsive coupling, anti-phase synchronization of spatiotemporal structures was observed for all considered combinations of intra-layer coupling. The correlation coefficient between symmetrical pairs of network nodes tended to be close to -1 in the case of anti-phase synchronization. The form of synchronous structures depended on the intra-layer coupling strengths, which varied with the repulsive inter-layer coupling.
Article
Mathematics, Applied
I. A. Shepelev, S. S. Muni, T. E. Vadivasova
Summary: This study investigates the synchronization effects in a heterogeneous two-layer network with attractive and repulsive inter-layer couplings, revealing the competition and mutual impact between two different types of couplings.
Article
Mechanics
Benmesbah Yasmine, Wantao Jia, Yong Xu
Summary: We investigate the synchronization behavior of a simple yet useful collective behavior mode in ensembles of interacting dynamical elements, namely the Kuramoto model with attractive-repulsive frequencies. By deriving a series of phase-locked states and determining the significant synchronization transition points with precise boundary conditions, we analyze the stability of the model and observe the bifurcation of the phase-locked states set. Interestingly, we find that these frequencies do not affect the stability of the system model but significantly alter its synchronization ability.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Mathematics, Applied
Jose A. Carrillo, Ruiwen Shu
Summary: We study the characteristics of a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. We provide explicit formulas for their associated global energy minimizers, whose supports are determined by ellipses under certain assumptions. By parameterizing the anisotropic part, we characterize the range in which these configurations are the global minimizers based on linear convexity arguments. Moreover, we observe that for certain anisotropic parts, the global minimizer is only given by vertically concentrated measures for large parameter values. We also discover an interesting gap of parameters between the collapse of the ellipse-supported configurations and the critical value for convexity. Additionally, we analyze the properties of superlevel sets and the behavior of global minimizers for certain anisotropic parts. These results extend and generalize previous findings in the literature, and numerical examples further explore even more complex behavior of anisotropic parts.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Physics, Fluids & Plasmas
Thomas Peron
Summary: Researchers studied the collective dynamics of phase oscillators on globally coupled networks with asymmetric interactions, identifying traveling wave and pi-states, as well as bistability between fully synchronized and incoherent states, in addition to chimera-like states not captured by the Ott-Antonsen theory for certain parameters and initial conditions.
Article
Mathematics, Interdisciplinary Applications
Amit Sharma, Biswambhar Rakshit
Summary: This study investigates the dynamical robustness in a network of oscillators with both attractive and repulsive coupling. The findings reveal complex aging transition dynamics due to the interplay of attractive and repulsive interactions. The aging transition occurs through both homogeneous and inhomogeneous steady states, with discontinuous phase transitions observed in the latter case.
CHAOS SOLITONS & FRACTALS
(2022)
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
Hyunsuk Hong, Kangmo Yeo, Hyun Keun Lee
Summary: In a system of random coupled oscillators, adjusting the ratio of positive to negative couplings can achieve a phase transition from incoherent to fully synchronized states, with the critical threshold predicted through linear stability analysis. Random couplings induce long-term state patterns, causing oscillators to move based on the location of the quenched couplings. Additionally, systems with mixed randomness for quenched couplings exhibit a combination of deformed patterns understandable through each annealed average.
Article
Physics, Multidisciplinary
Di Huang, Kevin Sampson, Yue Ni, Zhida Liu, Danfu Liang, Kenji Watanabe, Takashi Taniguchi, Hebin Li, Eric Martin, Jesper Levinsen, Meera M. Parish, Emanuel Tutuc, Dmitry K. Efimkin, Xiaoqin Li
Summary: When mobile impurities are introduced and coupled to a Fermi sea, new quasiparticles called Fermi polarons are formed. There are two regimes of the Fermi polaron problem: attractive polarons (AP) connected to pairing phenomena, and repulsive polarons (RP) responsible for ferromagnetism. In this study, we investigate Fermi polarons in a doped MoSe2 monolayer and find agreement with polaron theory for attractive polarons. The dynamics of Fermi polarons are important for understanding pairing and magnetic instabilities in various physical systems.
Article
Physics, Fluids & Plasmas
Sayantan Nag Chowdhury, Sarbendu Rakshit, Javier M. Buldu, Dibakar Ghosh, Chittaranjan Hens
Summary: This article explores the synchronization properties of dynamical systems connected through multiplex architectures, showing the coexistence of intralayer synchronization and antiphase dynamics between coupled systems of different layers. The transition from interlayer antisynchronization to antiphase synchrony in bipartite multiplex architectures is demonstrated, along with the necessary conditions and local stability analysis of the interlayer antisynchronization state.
Article
Engineering, Multidisciplinary
Suman Saha
Summary: This study investigates the resilience of a multiplex network consisting of identical dynamical units against parameter perturbation by adding selective linear diffusive cross-coupling links. The authors propose a recovery strategy that saves synchrony in the network from the edge of failure due to parameter mismatch by selectively adding cross-coupling links. The study extends this concept to 2-layered multiplex networks and enhances the stability of synchronous states from local to global stability. Analytical results and numerical simulations of two examples demonstrate the efficacy of the proposed coupling scheme.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2022)
Article
Mathematics, Applied
Seung-Yeal Ha, Dohyun Kim, Jaeseung Lee, Se Eun Noh
Summary: This study examines the emergent dynamics of a mixed Kuramoto ensemble with attractive and repulsive coupling strengths, finding that complete bi-polar synchronization can be achieved when considering coupling between two ensembles. The research relies on gradient-like flow formulation and energy estimate for the modeling perspective of the Kuramoto model.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mathematics, Applied
Mousumi Roy, Swarnendu Mandal, Chittaranjan Hens, Awadhesh Prasad, N. V. Kuznetsov, Manish Dev Shrimali
Summary: In this article, a data-driven approach using echo state network (ESN) is investigated to infer the dynamics of multistable systems. The machine is able to predict diverse dynamics for different parameter values, even at distant parameters from the training dynamics. The whole bifurcation diagram can also be accurately predicted. Additionally, the study extends to exploring the dynamics of co-existing attractors at unknown parameter values and identifying the basins for different attractors.
Article
Mathematics, Applied
Sourin Chatterjee, Sayantan Nag Chowdhury, Dibakar Ghosh, Chittaranjan Hens, Chittaranjan Hens
Summary: This article explores the impact of higher-order interactions on the evolution of social phenotypes and presents a new perspective for understanding this phenomenon. The study shows that perturbations have a significant influence on the coexistence equilibrium of competing species and can lead to the system being split into multiple feasible cluster states, depending on the number of perturbations.
Article
Mathematics, Applied
Arnob Ray, Timo Broehl, Arindam Mishra, Subrata Ghosh, Dibakar Ghosh, Tomasz Kapitaniak, Syamal K. Dana, Chittaranjan Hens
Summary: The role of topological heterogeneity in the origin of extreme events in a network is investigated. High degree nodes are vulnerable to weak repulsive interactions, while low degree nodes are susceptible to strong interactions. The occurrence of extreme events depends on the interplay between topological heterogeneity and repulsive interaction, and the formation position of extreme events shifts from high degree nodes to low degree nodes as the strength of repulsive interaction increases.
Article
Mathematics, Applied
Subrata Ghosh, Pitambar Khanra, Prosenjit Kundu, Peng Ji, Dibakar Ghosh, Chittaranjan Hens
Summary: We investigate epidemic spreading in heterogeneous networks with higher-order interactions and provide a recipe for constructing a reduced model. The microscopic state of nodes inversely scales with their degree and becomes diminished due to higher-order interactions, resulting in an abrupt transition in the macroscopic state. We also quantify the network's resilience and propose an alternative dimension reduction framework based on spectral analysis.
Article
Mathematics, Applied
Debarghya Pattanayak, Arindam Mishra, Nandadulal Bairagi, Syamal K. Dana
Summary: This paper discusses the statistics of transient dynamics in a classic tri-trophic food chain with bistability. It is found that the distribution of the transient time to predator extinction exhibits interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. Two new metrics, homogeneity index and local isotropic index, are introduced to characterize the distinctive features of the distribution. The paper also explains the origin of multimodal distributions and presents their ecological implications.
Correction
Mathematics, Applied
Sourin Chatterjee, Sayantan Chowdhury, Dibakar Ghosh, Chittaranjan Hens
Article
Physics, Multidisciplinary
Chandrakala Meena, Chittaranjan Hens, Suman Acharyya, Simcha Haber, Stefano Boccaletti, Baruch Barzel
Summary: The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Real-world networks often appear random and irregular, but the principles underlying their stability can be revealed through the study of the stability matrix. The dynamic Jacobian ensemble allows for systematic investigation of the fixed-point dynamics of network-based models, revealing discrete stability classes and the importance of scale and heterogeneity in ensuring stability.
Article
Multidisciplinary Sciences
Sanjeev K. Sharma, Argha Mondal, Eva Kaslik, Chittaranjan Hens, Chris G. Antonopoulos
Summary: This research establishes a fractional-order excitable neuron model with Caputo's fractional derivative and analyzes its effects on neuron characteristics. The findings indicate that the effect of fractional-order depends on synaptic connectivity and the memory trace of the system. Furthermore, the dynamics capture spike frequency adaptation and spike latency occurring over multiple timescales, which aligns with observations in neural computation.
SCIENTIFIC REPORTS
(2023)
Review
Mathematics, Applied
Arindam Mishra, Suman Saha, Syamal K. Dana
Summary: Chimera phenomenon has been extensively studied and experimentally verified in network dynamics. Chimera patterns have been observed in both non-locally coupled networks and globally coupled networks, regardless of the size of the network.
Article
Physics, Fluids & Plasmas
Sayantan Nag Chowdhury, Sarbendu Rakshit, Chittaranjan Hens, Dibakar Ghosh
Summary: In this article, the synchronization and antisynchronization in a two-layer multiplex network are investigated. The study demonstrates the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and also shows that such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.
Article
Physics, Fluids & Plasmas
Arindam Mishra, Suman Saha, Subrata Ghosh, Syamal Kumar Dana, Chittaranjan Hens
Summary: Positive phase coupling attracts in-phase synchrony in a group of phase oscillators, while positive phase velocity coupling may lead to diametrically opposite phases. Negative phase velocity coupling is necessary for inducing synchrony or coherence. The study explores the contrarian roles of phase coupling and phase velocity coupling on the synchrony of networks of second-order phase oscillators using two model systems.
Article
Physics, Fluids & Plasmas
Mousumi Roy, Abhishek Senapati, Swarup Poria, Arindam Mishra, Chittaranjan Hens
Summary: In this study, an ESN is used to predict the collective burst synchronization of neurons. The results show that a limited number of nodal dynamics can capture the trend of burst synchronization. Furthermore, the impact of node selection and hyperparameters on the prediction process has been examined.
Article
Physics, Fluids & Plasmas
Sahil Islam, Argha Mondal, Mauro Mobilia, Sirshendu Bhattacharyya, Chittaranjan Hens
Summary: In the rock-paper-scissor model, natural death plays a significant role in determining the fate of the system, especially in relation to coexistence. By conducting Monte Carlo simulations on a two-dimensional lattice with cyclically competing species, the study reveals that the presence of mobility leads to spiral patterns in the spatial distribution and introduces new coexistence and extinction scenarios, emphasizing the joint effect of death rate and mobility.
