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1.
The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators. 相似文献
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Experiments were carried out on arrays of chaotic electrochemical oscillators to which global coupling, periodic forcing, and feedback were applied. The global coupling converts a very weakly coupled set of chaotic oscillators to a synchronized state with sufficiently large values of coupling strength; at intermediate values both intermittent and stable chaotic cluster states occur. Cluster formation and synchronization were also obtained by applying feedback and forcing to a moderately coupled base state. The three cases differ, however, in other details. The feedback and forcing also produce periodic cluster states and more than two clusters. Configurations of two (chaotic) clusters and two, three, or four (periodic) clusters were observed. (c) 2002 American Institute of Physics. 相似文献
4.
Guy Katriel 《Physica D: Nonlinear Phenomena》2008,237(22):2933-2944
We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the ‘right’ sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [A. Khadra, Y.X. Li, A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons, Biophys. J. 91 (2006) 74-83.], and to indirectly weakly-coupled λ-ω oscillators. 相似文献
5.
Michał Marszal Ashesh Saha Krzysztof Jankowski Andrzej Stefański 《The European physical journal. Special topics》2016,225(13-14):2669-2678
We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities. 相似文献
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以环形耦合Duffing振子系统为研究对象,分析了耦合振子间的同步演化过程.发现在弱耦合条件下,如果所有振子受到同一周期策动力的驱动,那么系统在经历倍周期分岔、混沌态、大尺度周期态的相变时,各振子的运动轨迹之间将出现由同步到不同步再到同步的两次突变现象.利用其中任何一次同步突变现象可以实现系统相变的快速判别,并由此补充了利用倍周期分岔与混沌态的这一相变对微弱周期信号进行检测的方法.
关键词:
Duffing振子
同步突变
相变
微弱信号检测 相似文献
7.
We study the dynamics of nonlinear oscillators indirectly coupled through a dynamical environment or a common medium. We observed that this form of indirect coupling leads to synchronization and phase-flip transition in periodic as well as chaotic regime of oscillators. The phase-flip transition from in- to anti-phase synchronization or vise-versa is analyzed in the parameter plane with examples of Landau-Stuart and Ro?ssler oscillators. The dynamical transitions are characterized using various indices such as average phase difference, frequency, and Lyapunov exponents. Experimental evidence of the phase-flip transition is shown using an electronic version of the van der Pol oscillators. 相似文献
8.
The behaviors of coupled oscillators, each of which has periodic
motion with random natural frequency in the absence of coupling, are
investigated when phase shifts are considered. In the system of
coupled oscillators, phase shifts are the same between different
oscillators. Synchronization and synchronization transition are
revealed with different phase shifts. Phase shifts play an important
role for this kind of system. When the phase shift α<0.5π,
the synchronization state can be attained by increasing the
coupling, and the system cannot reach the synchronization state
while α≥q0.5π. A clear scaling between complete
synchronization critical coupling strength K_pc and
α-0.5π is found. 相似文献
9.
We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research. 相似文献
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An increase of the coupling strength in the system of two coupled R?ssler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings on the surfaces of unstable tori, whereas transition from phase to lag synchronization is preceded by a decrease in the number of unstable periodic orbits. 相似文献
11.
We study the emergence of collective synchronization in large directed networks of heterogeneous oscillators by generalizing the classical Kuramoto model of globally coupled phase oscillators to more realistic networks. We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider the case of networks with mixed positive-negative coupling strengths. We compare our theory with numerical simulations and find good agreement. 相似文献
12.
以单向驱动耦合Lorenz振子一维链为研究对象,研究振子间的混沌同步行为. 数值计算结果表明,对于变量y驱动x的耦合方式,在合适的耦合强度下,会出现第一个振子和第二个振子不同步,而与次近邻非直接连接的振子(如第三个振子)近似同步. 进一步研究表明,出现这一现象的原因是在大耦合强度下,对于这种驱动方式,第一个振子和第二个振子间出现驱动单变量近似同步;虽然它们之间未出现所有变量的完全同步,但是驱动信号事实上已经传递下去了.
关键词:
Lorenz振子
混沌同步
近似同步 相似文献
13.
Gabriel H. Paissan 《Physica D: Nonlinear Phenomena》2008,237(6):818-828
We consider an extension of Kuramoto’s model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an oscillator, Kuramoto’s theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight of the contribution of each oscillator to the mean field, and the coupling of each oscillator to that field. We explicitly analyze the effects of correlations between those weights and couplings, and show that synchronization can be completely inhibited when they are strongly anti-correlated. Numerical results validate the theory, but suggest that finite-size effect are relevant to the collective dynamics close to the synchronization transition, where oscillators become entrained in synchronized frequency clusters. 相似文献
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The purpose of this paper is to study the special forms of multimode dynamics that one can observe in systems with resource-mediated coupling, i.e., systems of self-sustained oscillators in which the coupling takes place via the distribution of primary resources that controls the oscillatory state of the individual unit. With this coupling, a spatially inhomogenous state with mixed high and low-amplitude oscillations in the individual units can arise. To examine generic phenomena associated with this type of interaction we consider a chain of resistively coupled electronic oscillators connected to a common power supply. The two-oscillator system displays antiphase synchronization, and it is interesting to note that two-mode oscillations continue to exist outside of the parameter range in which oscillations occur for the individual unit. At low coupling strengths, the multi-oscillator system shows high dimensional quasiperiodicity with little tendency for synchronization. At higher coupling strengths, one typically observes spatial clustering involving a few oscillating units. We describe three different scenarios according to which the cluster can slide along the chain as the bias voltage changes. 相似文献
16.
Markus Brede 《Physica D: Nonlinear Phenomena》2010,239(18):1759-1765
The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators on the network systematically shift the critical point as well as the critical exponents characterizing the transition. Negative correlations imply an onset of synchronization for smaller coupling, whereas positive correlations shift the critical coupling towards larger interaction strengths. For negatively correlated oscillators the transition still exhibits critical behaviour similar to that of the all-to-all coupled Kuramoto system, while positive correlations change the universality class of the transition depending on the correlation strength. Crucially, the paper demonstrates that the synchronization behaviour is not only determined by the coupling architecture, but also strongly influenced by the oscillator placement on the coupling network. 相似文献
17.
Impulsive synchronization of coupled dynamical networks with nonidentical Duffing oscillators and coupling delays 总被引:1,自引:0,他引:1
This paper aims to investigate the synchronization problem of coupled dynamical networks with nonidentical Duffing-type oscillators without or with coupling delays. Different from cluster synchronization of nonidentical dynamical networks in the previous literature, this paper focuses on the problem of complete synchronization, which is more challenging than cluster synchronization. By applying an impulsive controller, some sufficient criteria are obtained for complete synchronization of the coupled dynamical networks of nonidentical oscillators. Furthermore, numerical simulations are given to verify the theoretical results. 相似文献
18.
本文讨论了一维闭合环上Kuramoto相振子在非对称耦合作用下同步区域出现的多定态现象. 研究发现在振子数N≤3情形下系统不会出现多态现象, 而N≥4多振子系统则呈现规律的多同步定态. 我们进一步对耦合振子系统中出现的多定态规律及定态稳定性进行了理论分析, 得到了定态渐近稳定解. 数值模拟多体系统发现同步区特征和理论描述相一致. 研究结果显示在绝热条件下随着耦合强度的减小, 系统从不同分支的同步态出发最终会回到同一非同步态. 这说明, 耦合振子系统在非同步区由于运动的遍历性而只具有单一的非同步态, 在发生同步时由于遍历性破缺会产生多个同步定态的共存现象. 相似文献
19.
We analyze the phenomenon of frequency clustering in a system of
coupled phase oscillators. The oscillators, which in the absence
of coupling have uniformly distributed natural frequencies, are
coupled through a small-world network, built according to the
Watts-Strogatz model. We study the time evolution and determine
variations in the transient times depending on the disorder of
the network and on the coupling strength. We investigate the
effects of fluctuations in the average frequencies, and discuss
the definition of the threshold for synchronization. We
characterize the structure of clusters and the distribution of
cluster sizes in the synchronization transition, and define
suitable order parameters to describe the aggregation of the
oscillators as the network disorder and the coupling strength
change. The non-monotonic behavior observed in some order
parameters is related to fluctuations in the mean frequencies. 相似文献
20.
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary
conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the
value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions
as well as for a chain with fixed ends. We compare the results with those calculated numerically.
相似文献