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Adaptive Synchronizability of coupled oscillators With Switching

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Adaptive Synchronizability of Coupled Oscillators With Switc...

Chimera states of phase oscillator populations with nonlocal higher-order couplings

第24届中国控制与决策会议

作者： Johan A.K. Suykens Department of Electrical Engineering （ESAT-SCD） Katholieke Universiteit LeuvenKasteelpark Arenberg 10 B-3001 Leuven Belgium

In this paper, we study the influence of switching couplings in synchronization of a random network of Kuramoto oscillators. The topology of the network is assumed to be time-varying and switched over time. In order to adjust the accuracy of the switching effect, we introduce a switching regulatory index which is combined with the local order parameter in each time interval to regulate the value of switching interval. Under this switching scheme, the network topology can be intermittently changed. Numerical simulations illustrate that phase synchronizability of Kuramoto oscillators can significantly be enhanced in Erds-Rnyi network topology and scale-free network topology, but only slightly enhanced in small-world network topology under the proposed scheme.

关键词： coupled oscillators Switching Coupling Small-World Network Synchronization

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Chinese Physics B 2024年第4期33卷 402-407页

作者：伍勇刚余华健郑志刚徐灿 School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China Institute of Systems Science and College of Information Science and Engineering Huaqiao UniversityXiamen 361021China

The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical ***, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial *** works have shown that higher-order interactions promote coherent ***, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent ***, we identify that the chimera states arise as a result of multi-attractors in dynamic ***, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera *** the observed results can be well described in terms of the dimension reduction *** study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.

关键词： synchronization complex system coupled oscillators phase transition

Relaxation dynamics of Kuramoto model with heterogeneous coupling

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Chinese Physics B 2019年第12期28卷 136-141页

作者： Tianwen Pan Xia Huang Can Xu Huaping Lu School of Physics and Electronic Engineering Jiangsu Normal UniversityXuzhou 221116China School of Mathematics and Physics North China Electric Power UniversityBeijing 102206China Institute of Systems Science and College of Information Science and Engineering.Huaqiao University Xiamen 361021China

The Landau damping which reveals the characteristic of relaxation dynamics for an equilibrium state is a universal concept in the area of complex system. In this paper, we study the Landau damping in the phase oscillator system by considering two types of coupling heterogeneity in the Kuramoto model. We show that the critical coupling strength for phase transition, which can be obtained analytically through the balanced integral equation, has the same formula for both cases. The Landau damping effects are further explained in the framework of Laplace transform, where the order parameters decay to zero in the long time limit.

关键词： synchronization coupled oscillators Landau damping

Relaxation oscillations induced by an order gap between exciting frequency and natural frequency

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Science China(Technological Sciences) 2017年第2期60卷 289-298页

作者： CHEN XiaoKe LI ShaoLong ZHANG ZhengDi BI QinSheng Faculty of Civil Engineering and Mechanics Jiangsu University Zhenjiang 212013 China Faculty of Science Jiangsu University Zhenjiang 212013 China

The main purpose of the paper is to display the relaxation oscillations, known as the bursting phenomena, for the coupled oscillators with periodic excitation with an order gap between the exciting frequency and the natural frequency. For the case when the exciting frequency is much smaller than the natural frequency, different types of bursting oscillations such as fold/fold, Hopf/Hopf bursting oscillations can be observed. By regarding the whole exciting term as a slow-varying parameter on the fact that the exciting term changes on a much smaller time scale, bifurcations sets of the generalized autonomous system is derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two cases with typical bifurcation patterns are focused on as examples to explore the dynamical evolution with the variation of the amplitude of the external excitation. Bursting oscillations which alternate between quiescent states (QSs) and repetitive spiking states (SPs) can be obtained, the mechanism of which is presented by introducing the transformed phase portraits overlapping with the bifurcation diagrams of the generalized autonomous system. It is found that not only the forms of QSs and SPs, but also the bifurcations at the transition points between QSs and SPs, may influence the structures of bursting attractors. Furthermore, the amplitudes and the frequencies related to SPs may depend on the bifurcation patterns from the quiescent sates.

关键词： coupled oscillators periodic excitation bursting oscillations bifurcation mechanism

Hopf Bifurcation in a Nonlinear Wave System

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Chinese Physics Letters 2004年第3期21卷 439-442页

作者：贺凯芬 KeyLaboratoryinUniversitiesforRadiationBeamTechnologyandMaterialsModification InstituteofLowEnergyNuclearPhysicsBeijingNormalUniversityBeijing100875

Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point. It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for further exploration of the routes to turbulence.

关键词： waves Exploration Fixed point Doppler effect coupled oscillators Turbulent Flow BIFURCATION Routes nonlinearity Wave equation

Bidirectionally coupled Synchronization of Delayed-Feedback oscillators

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Bidirectionally Coupled Synchronization of Delayed-Feedback ...

Phase Synchronization as a Mechanism of Controlling Spatiotemporal Chaos via External Periodic Signal

第二届全国复杂动态网络学术论坛

作者： Margaret C.Chiang How-Foo Chen Electrical Engineering Department University of California Los AngelesLos AngelesCA 90095U S.A

General synchronization scenarios of bidirectionaily coupled oscillators with delayed feedback are studied with all possible *** generic configurations are identified,with one of them reduced unidirectional coupling but the other three represent bidirectional *** conditions of synchronization for all scenarios are analyzed and summarized.

关键词： coupled oscillators synchronization chaos and laser dynamics

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Chinese Physics Letters 2004年第2期21卷 254-257页

作者：桑海波贺凯芬 TheKeyLaboratoryofBeamTechnologyandMaterialsModificationofEducationMinistry BeijingNormalUniversityBeijing100875 InstituteofLowEnergyNuclearPhysics BeijingNormalUniversityBeijing100875

We find that phase synchronization (PS) is a mechanism in which the spatiotemporal chaos (STC) can be suppressed to a spatially regular (SR) state by applying an external periodic signal in a one-dimensional driven drift-wave system. In the driving wave coordinate, the nonlinear system can be transformed to a set of coupled oscillators moving in a periodic potential. In this multi-dimensional system, the internal modes are slaved one by one through PS by the control signal. Two types of responses of the internal modes to the external periodic signal are observed. For some modes, the stabilization is through frequency-locking; while for the other modes, a special kind of PS without frequency-licking, namely multi-looping PS, is developed.

关键词： PERIODIC SIGNAL One-to-one correspondence Periodic coupled oscillators signals phase synchronization Polystyrenes Vibrations modes potential

Right on time:measuring Kuramoto model coupling from a survey of wrist-watches

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Chinese Physics B 2010年第10期19卷 386-389页

作者：史瑞吉 Bouchet-Franklin Research Institute P O Box 10051 Rochester NY 14610 USA

Using a survey of wrist-watch synchronization from a randomly selected group of independent volunteers, we model the system as a Kuramoto-type coupled oscillator network. Based on the phase data both the order parameter and likely size of the coupling are derived and the possibilities for similar research to deduce topology from dynamics are discussed.

关键词： coupled oscillators Kuramoto model complex networks synchronization

Chaos Synchronization in Complex Networks

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Chinese Physics Letters 2005年第9期22卷 2183-2185页

作者：杨俊忠章梅 School of Science Beijing University of Posts and Telecommunications Beijing 100088 Center for Advanced Study Tsinghua University Beijing 100084

We employ several simple numerical experiments to show that the statements that short mean path length or low heterogeneity enhances synchronizability in complex networks could be misleading. Furthermore, we point out that the impacts of the structural parameters on the synchronizability are complicated even if we could change one structural parameter independently.

关键词： SMALL-WORLD NETWORKS coupled oscillators SYSTEMS INSTABILITY