Acta Physica Sinica, Volume. 68, Issue 18, 180503-1(2019)
Fig. 1. Coupled star networks: (a) Single star network; (b) two coupled networks; (c) multiple coupled networks.耦合星型网络示意图 (a)单个星型网络; (b)两个耦合星型网络; (c)多个耦合星型网络
Fig. 2. Numerical results for
,
. (a)−(e) Average frequency versus coupling strength for two coupled star networks
Fig. 3. (a)−(c) versus . (d) versus , where ; the parameter space can be divided into different regions according to the value of ; the red lines denote ; the black lines denote ; the white lines denote . (a)−(c)分别表示 随 值的变化情况; (d) 随 值的变化情况, , 参数平面被分为不同的区域, 两条红线表示 与 相等的区域, 两条黑线表示 与 相等的区域, 白线表示 与 相等的区域
Fig. 4. Relationship between and . 系统的临界耦合强度 随 值的变化情况
Fig. 5. Logarithmic variance of average frequency in parameter space of coupling strength for : (a) ; (b) ; (c) ; (d) . The smaller logarithmic variance of average frequency indicates better synchronization. Black line, white line and green line represent the theoretical critical coupling strength for synchroniation , , , respectively. 时, 不同耦合强度参数区间下, 节点平均频率的方差的对数值 (a) ; (b) ; (c) ; (d) , 颜色越靠近冷色调表示系统的同步程度越高, 黑线、白线、绿线分别表示理论推导出的 , ,
Fig. 6. Numerical results and theoretical results for , , [0.77, 0.80, 0.19, 0.49]: (a) The critical coupling strength for synchronization versus the summation of central node frequencies; the numerical results are shown in the circle and the theoretical ones are shown in the solid lines; (b) the logarithmic variance of average frequency in parameter space of for given . 参数为 [0.77, 0.80, 0.19, 0.49]时的数值计算结果 (a)控制所有耦合强度相等时, 系统的同步临界耦合强度随 的和的关系图, 数值计算结果如圆圈所示, 理论推导结果如实线所示; (b)当固定 , 改变参数 时, 所有节点平均频率的方差的对数结果, 绿线和白线分别是理论得到的
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Rui Shu, Wei Chen, Jing-Hua Xiao.
Received: Mar. 5, 2019
Accepted: --
Published Online: Jun. 28, 2020
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