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phase synchronization on small-world networks with community structure

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Chinese Physics B 2010年第2期19卷 92-100页

作者：王晓华焦李成吴建设 Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China Xidian University Aeronautical Computing Technique Research Institute

In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region （r ≤ 0.001）, the network has even worse synchronizability than the case of isolated communities （r = 0）. Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales： the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network.

关键词： complex networks small-world community structure phase synchronization

phase synchronization and its transition in two coupled bursting neurons:theoretical and numerical analysis

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Chinese Physics B 2010年第6期19卷 130-138页

作者：王海侠陆启韶石霞 School of Science Nanjing University of Science and Technology Department of Dynamics and Control Beihang University School of Science Beijing University of Posts and Telecommunications

It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris-Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.

关键词： phase synchronization synchronization transition bifurcation diagram

phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

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Chinese Physics B 2013年第7期22卷 79-83页

作者： Hossein Gholizade-Narm Asad Azemi Morteza Khademi Faculty of Electrical Electronic & Robotic EngineeringShahrood University Technology College of Engineering Penn State University Faculty of Engineering Ferdowsi University of Mashhad

In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.

关键词： van der Pol oscillator delay coupling phase synchronization synchronization frequency

phase synchronization in Electrically Coupled Different Neuronal Pacemakers with the Chay Model

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Chinese Physics Letters 2005年第3期22卷 547-550页

作者：石霞陆启韶 SchoolofScience BeijingUniversityofAeronauticsandAstronauticsBeijing100083

We study the phase synchronization in different electrically coupled neuronal pacemakers with the Chay model. The numerical simulation results and the definition of the mean frequency show that phase synchronization is equal to the mean frequency locking. Nearly complete synchronization of different two coupled neuronal pacemakers is also investigated. It is shown that the cross-correlation of the membrane potential variables is suitable to judge the nearly complete synchronization.

关键词： phase synchronization Electrically Coupled Different Neuronal Pacemakers Chay Model

phase synchronization of Coupled Rossler Oscillators： Amplitude Effect

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Communications in Theoretical Physics 2007年第2期47卷 265-269页

作者： LI Xiao-Wen ZHENG Zhi-Gang Department of Physics and the Beijing-Hong-Kong-Singapore Joint Center for Nonlinear and Complex Systems （Beijing） Beijing Normal University Beijing 100875 China

phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored. It is found that depending on parameter mismatches, the synchronization of phases exhibits different manners. The synchronization regime can be divided into three regimes. For small mismatches, the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases, the amplitudes and phases of oscillators are correlated） and the amplitudes will dominate the synchronous dynamics for very large mismatches. The lag time among phases exhibits a power law when phase synchronization is achieved.

关键词： phase synchronization amplitude eiiect

phase synchronization of Chua circuit induced by the periodic signals

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Chinese Physics B 2005年第1期14卷 55-60页

作者：王世红刘维清马宝军肖井华蒋达娅 ScienceSchool BeijingUniversityofPostsandTelecommunicationsBeijing100876China

phase synchronization of chaotic systems induced by periodic signals is studied experimentally and *** kinds of periodic signals are chosen to drive Chua circuits, including the periodic signal in the Chua circuit,sinusoidal and pulsed signals. Under conditions of small mismatch between the natural frequencies of the periodic and the chaotic signals, appropriate amplitudes of the driving signals, and appropriate duty cycles of the pulse, phase synchronization can be achieved. Even when the duty circle reduces to 3%, it can still drive the chaotic signals into phase synchronization, which is interesting for applications.

关键词： phase synchronization chaotic oscillator

Transition to phase synchronization Through Generalized synchronization

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Chinese Physics Letters 2003年第7期20卷 999-1002页

作者：何岱海张廷宪高建郑志刚 DepartmentofMathematicsandStatistics mcMasteruniversityHamiltonL8S4K1Canada DepartmentofPhysics BeijingnormalUniversityBeijing100875 DepartmentofPhysics QujingNormalCollegeQujing655000 DepartmentofPhysics BeijingnormalUniversityBeijing100875

synchronization in drive-response chaotic systems is studied. For a small mismatch of the natural frequency of the drive and response oscillators, phase synchronization comes before generalized synchronization. For moderate and even large parameter misfits, generalized synchronization can be achieved before phase synchronization. The mechanism of these two different bifurcations is interpreted in terms of the local-minimal-fluctuation method. It is found that the qualitative changes of local-minimal-fluctuations of the response system well manifests the appearance of generalized synchronization.

关键词： Transition phase synchronization Generalized synchronization

Complete and phase synchronization in a heterogeneous small-world neuronal network

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Chinese Physics B 2009年第2期18卷 482-488页

作者：韩芳陆启韶 Wiercigroch Marian 季全宝 School of Science Beijing University of Aeronautics and Astronautics School of Engineering University of Aberdeen

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.

关键词： small-world neuronal network complete synchronization phase synchronization het erogeneity

Discrimination of Motor Imagery Patterns by Electroencephalogram phase synchronization Combined With Frequency Band Energy

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IEEE/CAA Journal of Automatica Sinica 2017年第3期4卷 551-557页

作者： Chuanwei Liu Yunfa Fu Jun Yang Xin Xiong Huiwen Sun Zhengtao Yu Faculty of Information Engineering and Automation Kunming University Science and Technology Shanghai Micro Electronics Equipment Co. Ltd. (SMEE)

Central nerve signal evoked by thoughts can be directly used to control a robot or prosthetic devices without the involvement of the peripheral nerve and *** is a new strategy of human-computer interaction.A method of electroencephalogram(EEG) phase synchronization combined with band energy was proposed to construct a feature vector for pattern recognition of brain-computer interaction based on EEG induced by motor imagery in this paper,rhythm and beta rhythm were first extracted from EEG by band pass filter and then the frequency band energy was calculated by the sliding time window;the instantaneous phase values were obtained using Hilbert transform and then the phase synchronization feature was calculated by the phase locking value(PLV) and the best time interval for extracting the phase synchronization feature was searched by the distribution of the PLV value in the time ***,discrimination of motor imagery patterns was performed by the support vector machine(SVM).The results showed that the phase synchronization feature more effective in4s-7s and the correct classification rate was 91.4%.Compared with the results achieved by a single EEG feature related to motor imagery,the correct classification rate was improved by 3.5 and4.3 percentage points by combining phase synchronization with band *** indicate that the proposed method is effective and it is expected that the study provides a way to improve the performance of the online real-time brain-computer interaction control system based on EEG related to motor imagery.

关键词： Brain-computer interaction(BCI) electroencephalogram(EEG) frequency band energy motor imagery phase synchronization