液面上耦合振子系统的同步模式  

Synchronized modes of coupled oscillator system on liquid surface

作　　者：董蔚 童浩轩 张皓玥 彭韵茹 狄增如[1,2] DONG Wei;TONG Haoxuan;ZHANG Haoyue;PENG Yunru;DI Zengru(Faculty of Arts and Sciences,International Academic Center of Complex Systems,Advanced Institute of Natural Sciences,Beijing Normal University,519087,Zhuhai,Guangdong,China;School of Systems Science,Beijing Normal University,100875,Beijing,China)

机构地区：[1]北京师范大学文理学院,北京师范大学自然科学高等研究院复杂系统国际科学中心,广东珠海519087 [2]北京师范大学系统科学学院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2023年第1期9-12,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金重点资助项目(71731002)。

摘　　要：利用MATLAB对耦合双节拍器系统模型的动力学方程组进行了数值模拟,发现初始条件决定了系统达到稳态时所呈现的同步模式;探究了液体的黏滞阻力与耦合板的质量对系统同步模式的影响,黏滞阻力的大小与稳态时为反相同步的概率呈正相关关系;耦合板质量与稳态时为反相同步的概率呈负相关关系;在弛豫时间方面,发现同相同步比反相同步的平均弛豫时间更慢;在实验上,搭建液面上的耦合振子系统,使用水、质量分数为10%的盐水和食用油3种黏滞系数不同的液体进行实验,定性地得到了与数值模拟一致的结果.In this article,a coupled oscillator system model was adopted,and its dynamics equations were numerically simulated with MATLAB.The initial conditions of the system determined the synchronization mode when the system reached steady state.Simulation on viscous resistance of liquid and quality of coupling plate showed that viscous resistance was positively correlated with probability of anti-phase synchronization,mass of coupling plate was negatively correlated with probability of anti-phase synchronization in steady state.In terms of relaxation time,it was found that average relaxation time of in-phase synchronization was slower than anti-phase synchronization.A coupled oscillator system was set up on the surface of the liquid,and three kinds of liquid with different viscosity coefficients,water,salt water with a concentration of 10%and cooking oil,were used.Experimental results are qualitatively consistent with numerical simulations.

关 键 词：耦合振子系统 非线性系统 同步状态 弛豫时间 

分 类 号：O322[理学—一般力学与力学基础]