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摘要

对多粒子耦合系统而言, 环境涨落对各粒子的作用在实际情况中往往是互异的, 为此, 本文研究不同频率涨落驱动下全局耦合过阻尼谐振子系统中的集体动力学行为, 包括稳定、同步和随机共振. 通过随机平均法推导得出粒子行为的统计同步性, 进而得到了系统平均场与单粒子行为在统计意义下的等价性. 并且, 利用该同步性进一步求解得到了输出幅值增益和系统稳定的充要条件. 前者为分析系统随机共振行为奠定了理论基础, 后者给出了本文所得结论的适应范围. 仿真表明, 耦合强度 $\varepsilon$ 的增加或系统规模 N的增大会带来两方面的影响: 首先, 稳定区域逐渐增大, 同步时间逐渐缩短; 其次, 系统的有序性增强, 需要更大的噪声强度提供更强的随机性来与之实现最优匹配, 从而关于噪声强度 $\sigma$ 的随机共振峰逐渐右移, 反之亦然.

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Abstract

For multi-particle coupled systems, the effects of environmental fluctuations on each particle are often different in actual situations. To this end, this paper studies the collective dynamic behaviors in globally coupled harmonic oscillators driven by different frequency fluctuations, including synchronization, stability and stochastic resonance (SR). The statistical synchronicity between particles' behaviors is derived by reasonably grouping variables and using random average method, and then the statistical equivalence between behaviors of mean field and behaviors of single particle is obtained. Therefore, the characteristics of mean field's behaviors (that is, collective behaviors) can be obtained by studying behaviors of any single particle. Moreover, the output amplitude gain and the necessary and sufficient condition for the system stability are obtained by using this synchronization. The former lays a theoretical foundation for analyzing the stochastic resonance behavior of the system, and the latter gives the scope of adaptation of the conclusions in this paper. In terms of numerical simulation, the research is mainly carried out through the stochastic Taylor expansion algorithm. Firstly, the influence of system size Nand coupling strength $\varepsilon$ on the stability area and synchronization time is analyzed. The results show that with the increase of the coupling strength $\varepsilon$ or the increase of the system size N, the coupling force between particles increases, and the orderliness of the system increases, so that the stable region gradually increases and the synchronization time gradually decreases. Secondly, the stochastic resonance behavior of the system is studied. Noises provide randomness for the system, and coupling forces provide orderliness for the system. The two compete with each other, so that the system outputs about the noise intensity $\sigma$ , the coupling strength $\varepsilon$ and the system size Nexhibit stochastic resonance behavior. As the coupling strength increases or the system size increases, the orderliness of the system increases, and greater noise intensity is required to provide stronger randomness to achieve optimal matching with it, so as to the resonance of the noise intensity $\sigma$ , the peak gradually shifts to the right. Conversely, as the noise intensity $\sigma$ increases, the resonance peak of the coupling strength $\varepsilon$ and the system size Nwill also shift to the right.

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作者及机构信息

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通信作者:蔚涛,scuyutao@163.com

基金项目:国家自然科学基金青年基金(批准号: 11501385, 11801385)资助的课题

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Corresponding author:Yu Tao,scuyutao@163.com

Funds:Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11501385, 11801385)

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参考文献

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施引文献

下载: 全尺寸图片幻灯片

乘因子	变量
1	$ \left\langle x_1\right\rangle $	$ \cdots $	$ \left\langle x_i\right\rangle $	$ \cdots $	$ \left\langle x_N\right\rangle $
$ \xi_1 $	$ \left\langle \xi_1 x_1\right\rangle $	$ \cdots $	$ \left\langle \xi_1 x_i\right\rangle $	$ \cdots $	$ \left\langle \xi_1 x_N\right\rangle $
$ \vdots $	$ \vdots $	$ \vdots $			$ \vdots $
$ \xi_{i_1}\xi_{i_2}\cdots\xi_{i_k} $	$ \left\langle \xi_{i_1}\xi_{i_2}\cdots\xi_{i_k}x_1\right\rangle $	$ \cdots $	$ \left\langle \xi_{i_1}\xi_{i_2}\cdots\xi_{i_k}x_i\right\rangle $	$ \cdots $	$ \left\langle \xi_{i_1}\xi_{i_2}\cdots\xi_{i_k}x_N\right\rangle $
$ \vdots $	$ \vdots $	$ \vdots $			$ \vdots $
$ \xi_{1}\xi_{2}\cdots\xi_{N} $	$ \left\langle \xi_{1}\xi_{2}\cdots\xi_{N}x_1\right\rangle $	$ \cdots $	$ \left\langle\xi_{1}\xi_{2}\cdots\xi_{N}x_i\right\rangle $	$ \cdots $	$ \left\langle \xi_{1}\xi_{2}\cdots\xi_{N}x_N\right\rangle $

下载: 导出CSV

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