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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (3): 307-320.doi: 10.3969/j.issn.1005-3085.2017.03.007

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复杂网络的牵制同步（英）

邢志伟1,   彭济根2   

  1. 1- 西安工程大学理学院，西安  710048
    2- 西安交通大学数学与统计学院，西安  710049
  • 收稿日期:2015-12-15 接受日期:2016-11-21 出版日期:2017-06-15 发布日期:2017-08-15
  • 基金资助:
    国家自然科学基金(11271297; 11302158; 11501435)；陕西省自然科学基金(2015JM1012; 2015 jm1034)；陕西省教育厅自然科学基金(2013JK0591).

Pinning Synchronization of Complex Networks

XING Zhi-wei1,   PENG Ji-gen2   

  1. 1- School of Science, Xi'an Polytechnic University, Xi'an 710048
    2- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2015-12-15 Accepted:2016-11-21 Online:2017-06-15 Published:2017-08-15
  • Supported by:
    The National Natural Science Foundation of China (11271297; 11302158; 11501435); the Natural Science Foundation of Shaanxi Province (2015JM1012; 2015JM1034); the Natural Science Foundation of Shaanxi Provincial Education Department (2013JK0591).

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摘要： 本文主要研究了复杂网络的牵制同步问题．通过定义一个新的非线性算子的非线性$P$-测度，得到了一系列保证复杂网络在牵制控制下全局同步的充分条件．所得结果不要求耦合矩阵的对称可约性以及函数的连续可微性．因此，在复杂网络的牵制同步控制中具有更广的使用范围．最后我们通过两个实例来验证所得结论的有效性．

关键词: 非线性测定, 复杂网络, 牵制控制

Abstract: This paper is concerned with the pinning synchronization problem of complex networks. By defining a new nonlinear $P$-measure of the nonlinear operator, a set of sufficient conditions are obtained to guarantee the global synchronization of the pinning process. The obtained results do not require the symmetric irreducibility of the coupling matrix and the continuous differentiability of functions. Therefore a broader application domain for the pinning synchronization of complex networks is provided. Finally, two simulation examples of complex networks are presented to demonstrate our theoretical results.

Key words: nonlinear measure, complex network, pinning synchronization

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