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Synchronization of coupled metronomes on two layers

Frontiers of physics 2017年第6期12卷 53-62页

作者： Jing Zhang Yi-Zhen yu Xin-Gang Wang School of Physics and Information Technology Shaanxi Normal University Xi'an 710062 China

coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of com- plex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization （SS） state, the generalized splay synchronization （GSS） state, the anti-phase synchronization （APS） state, the in-phase delay synchronization （IPDS） state, and the in-phase syn- chronization （IPS） state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.

关键词： coupled oscillators experimental study synchronization pattern

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Hopf Bifurcation Analysis in coupled Van der Pol-Duffing oscillators with two delays

Hopf Bifurcation Analysis in coupled Van der Pol-Duffing osc...

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第十五届全国非线性振动暨第十二届全国非线性动力学和运动稳定性学术会议

作者：魏周超 ZHANG Wei School of Mathematics and Physics China University of Geosciences College of Mechanical Engineering Beijing University of Technology

In this paper,a four-dimensional coupled Van der Pol-Duffing oscillators with two delays is *** main result is given in terms of local stability and Hopf *** conditions for local stability of the zero equilibrium and existence of the Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic *** particular,explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold *** addition,it is found that when delay passes through these critical values,chaotic oscillations are converted into a stable periodic *** numerical examples are also presented to verify the theoretical analysis.

关键词： coupled oscillators Hopf Bifurcation Time delay Periodic solution Chaos

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Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

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Communications in Theoretical Physics 2008年第10期50卷 903-906页

作者： ZHANG Ji-Qian CHEN Han-Shuang WANG Mao-Sheng College of Physics and Electronic Information Anhui Normal University Wuhu 241000 China

We consider the dynamics of locally coupled calcium oscillation systems,each cell is subjected to extracel-lular contaminated signal,which contains common sub-threshold signal and independent Gaussian *** is found thatintermediate noise can enhance synchronized oscillations of calcium ions,where the frequency of noise-induced oscilla-tions is matched with the one of sub-threshold external *** show that synchronization is enhanced as a result ofthe entrainment of external signal Furthermore,the effect of coupling strength is *** find above-mentionedphenomenon exists only when coupling strength is very *** findings may exhibit that noise can enhance thedetection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.

关键词： synchronization noise coupled oscillators random processes

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Effect of Transcription Cooperativity on Population Behavior

Effect of Transcription Cooperativity on Population Behavior

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第36届中国控制会议

作者： Qizhi Yi Yan Du College of Mathematics and Information Science Jiangxi Normal University College of Chemistry and Chemical Engineering Jiangxi Normal University

ISBN: (纸本)9781538629185

There are many factors that affect the population behavior of *** for the ways of cellular communication and the cellular environment,which have been considered in the previous studies,transcription cooperativity（or Hill coefficient） that has been little considered before is also an important *** article investigates the effects of Hill coefficient on dynamical behavior in a synthetic multicellular system,where individual oscillators are an integration of repressilators and hysteresis-based oscillators and they are coupled through a quorum-sensing *** bifurcation analysis and numerical simulation,we find that because of the variety of Hill coefficient the system can show five kinds of typical dynamical structures on cell density,which suggests that Hill coefficient has great influences not only on the systems ability to oscillate and the modes of oscillation but also on the occurrence of *** increasing Hill coefficient,the system evolves along the route from monostability to switches among monostability,bistability and multistability,from non-oscillation to simple oscillation,from a single oscillating mode to switches among a variety of oscillating *** results may be the foundation for understanding complicated collective behaviors of cells.

关键词： Transcription Cooperativity Quorum Sensing Population Behavior coupled oscillators

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Synchronization dynamics of phase oscillators with generic adaptive coupling

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Communications in Theoretical Physics 2023年第4期75卷 114-122页

作者： Xin Jin Yong-Gang Wu Hua-Ping Lü Can Xu School of Physics and Electronic Engineering Jiangsu Normal UniversityXuzhou 221116China School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China Institute of Systems Science and College of Information Science and Engineering Huaqiao UniversityXiamen 361021China

Adaptive coupling schemes among interacting elements are ubiquitous in real systems ranging from physics and chemistry to neuroscience and have attracted much attention in recent ***,we extend the Kuramoto model by considering a particular adaptive scheme in a system of globally coupled *** homogeneous coupling is correlated with the global coherence of the population that is weighted by the generic nonlinear feedback function of the amplitude of the order *** studied model is analytically tractable that generalizes the theory of Kuramoto for synchronization *** develop a mean-field theory by establishing the self-consistent equation describing the stationary dynamics in the thermodynamic ***,the Landau damping effect,which turns out to be far more generic,is revealed in the framework of the linear stability analysis of the resonant pole ***,the relaxation rate of the order parameter in the subcritical region is obtained from a universal *** study can deepen the understanding of synchronization transitions and other related collective dynamics in networked oscillators with adaptive interaction schemes.

关键词： synchronization complex system coupled oscillators phase transition

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Modification of energy balance equations in Statistical Energy Analysis

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Chinese Journal of Acoustics 1996年第1期15卷 1-7页

作者： SUN Jincai WANG Chong and SUN Zhaohui (Institute of Acoustic Engineering Northwestern Polytechnical University Xi’an, 710072)

The energy balance equations in the Classical Statistical Energy Analysis (CSEA) are modified by the equations of power flow among the thtee serial coupled oscinators. The modified equations include not only the direct power flow, but also the indirect power flow. The parameters in the modified equations can be expressed by those in the classical equations when the accuracy of the predicted results is able to satisfy the needs for ellgineering.

关键词： Energy balance equations Statistical Energy Analysis Power flow coupled oscillators

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Nonlinear Active Antenna

Nonlinear Active Antenna

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2007 IEEE International Workshop on Anti-counterfeiting,Security,Identification

作者： Ling Xiang Jiang Yonghua Jiang Zhisheng Gao Weiliang Naval Aeronautical Engineering Institute Yantai 264001 China

A new nonlinear active antenna is presented. The dynamics of nonlinear active phase array based on coupled oscillators and coupled phase locked loop are analyzed. Tuning the free-running frequencies of the edge oscillators, a constant phase gradient between the adjacent oscillators can be obtained. This new antenna can achieve beam-scanning without phase-shifter. Two experimental circuits are also shown.

关键词： nonlinear coupled oscillators coupled PLL beam-scanning

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