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1.
A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained. 相似文献
2.
Jürgen Kurths M. Carmen Romano Marco Thiel Grigory V. Osipov Mikhail V. Ivanchenko István Z. Kiss John L. Hudson 《Nonlinear dynamics》2006,44(1-4):135-149
We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent
oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences
of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel
regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach
to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In
order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data
from a population of 64 electrochemical oscillators. 相似文献
3.
R. L. Dobrushin A. Pellegrinotti Yu. M. Suhov L. Triolo 《Journal of statistical physics》1988,52(1-2):423-439
The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived. 相似文献
4.
Kenzo Sato 《International Journal of Infrared and Millimeter Waves》1986,7(6):927-947
Under the influence of perpendicularly applied positive electro-static field less than 103V/cm to silk fibron textiles, at the high frequency side of the C2–O bending reflection band (450350 cm–1), effect of step creation and step annihilation of the C2–O pseudo dending bands was induced in three stages at 600450 cm–1 region IR spectroscopically relating to the stepnized statistical transfer of the unbonded 2P2, electrons in carbon which present with density of 4.0×1014/cm2 in the surface mono-layer of silk fibroin from the states formed in (–C1–C2–N–)m spiral chains upto the pseudo-bending states formed in C2–O bondings. Fine 90 steps measured overlapping on these four types of C2–O reflection bands were analysed as to consist four step series and they were shown as,y = A·Jm + B cm–1 with A=20, B=521, m=0.55 and J=1, 2...18 for the B-series.And with A=39, B=283, m=0.63 and J=1, 2 ...17 for the C-series.y
J = A·J + B cm–1 with A=11.42, B=201 and J=1, 2...13, for the D-series. And, stepnized C2–O bending bands including that of permanent oscillators and pseudo-bending oscillators induced by the effect of transfer of the unbonded 2P2 electrons in carbon atoms were shown as, EN=A·N2+B·N+C (eV) with A=–1.50×10–3, B=1.65×10–2 and C=2.4×10–2. 相似文献
5.
B. Hlavőček J. Šestők L. Koudelka P. Mošner J. J. Mareš 《Journal of Thermal Analysis and Calorimetry》2005,80(2):271-283
Summary The forms of vibrations and displacements of particles in amorphous structures have been investigated. The particles, moving on highly non-linear amplitude, are responsible for the creation of disordered structures of amorphous bodies. The non-linear oscillators, even if 'few' in concentration, are characterized by unpredictable trajectories in phase space. The non-linear oscillators are fully developed in the liquid state above the crossover temperature Tcr and between Tcr and Tg their number decreases. Under Tg they completely disappear. The interconnection between the linear oscillators in blocks plays the most important role in the characteristic time spectra in liquid state. Using the additive properties of elements polarizibilities, the number of acoustical units in individual blocks at Tcr is estimated to be about 600 units. The diameter of blocks at Tcr was estimated to be about 1.8 nm. Even if the non-linear high amplitude motions disappear at solidification, the remnants of structural irregularity remain and the disordered structure of glass is formed. 相似文献
6.
Magorzata Bancewicz 《International journal of quantum chemistry》2002,88(6):742-749
The expressions for moments of spectral density distribution of a Hamiltonian representing a system of N coupled Morse oscillators are reduced to the large‐N limit. The effect of the values of coupling constants on the spectral density distribution is analyzed. For the values of coupling constants within the pertinent range for real molecules, the relations between moments appear to be close to those for a Gaussian distribution. Outside this range, the deviations from the normal distribution are substantial. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 相似文献
7.
V.K. Chandrasekar Jane H. Sheeba R. Gladwin Pradeep R.S. Divyasree M. Lakshmanan 《Physics letters. A》2012
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically. 相似文献
8.
Raquel M. López José M. Vega-Guzmán 《Journal of Difference Equations and Applications》2013,19(4):543-554
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented. 相似文献
9.
分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板(简称“分布振子复合板”),进而实现较宽的减振频带.对于多点支撑处受到宽频非一致激励(例如在不同激励点处的激励频率、幅值与相位有差异)的分布振子复合板,目前还缺乏有效简便的优化控制指标.在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化.本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性.首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性.而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响.最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应.结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性. 相似文献
10.