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,从而关于噪声强度的随机共振峰逐渐右移,反之亦然.
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 N and coupling strengthεon the stability area and synchronization time is analyzed.The results show that with the increase of the coupling strengthεor 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 intensityσthe coupling strengthεand the system size N exhibit stochastic resonance behavior.As the coupling strength increases or the system size increases,the orderliness of the system increases,and greater no
作者
姜磊
赖莉
蔚涛
罗懋康
Jiang Lei;Lai Li;Yu Tao;Luo Mao-Kang(College of Mathematics,Sichuan University,Chengdu 610064,China;School of Aeronautics and Astronautics,Sichuan University,Chengdu 610064,China)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2021年第13期29-44,共16页
Acta Physica Sinica
基金
国家自然科学基金青年基金(批准号:11501385,11801385)资助的课题.
关键词
全局耦合谐振子
随机共振
同步
稳定
stochastic resonance
globally coupled harmonic oscillators
synchronization
stability
