一类节点数不同的不确定时空网络的指数外同步

荣婷婷; 高艳; 颜哲

doi:10.21656/1000-0887.380230

一类节点数不同的不确定时空网络的指数外同步

doi: 10.21656/1000-0887.380230

辽宁师范大学物理与电子技术学院, 辽宁大连 116029

详细信息

作者简介:
荣婷婷（1992—），女，朝鲜族，硕士(通讯作者. E-mail: 421787800@qq.com).

中图分类号: O415
计量
- 文章访问数: 925
- HTML全文浏览量: 171
- PDF下载量: 521
- 被引次数: 0
出版历程
- 收稿日期: 2017-07-20
- 修回日期: 2017-11-14
- 刊出日期: 2018-02-15

A Class of Exponential Outer Synchronization Between Uncertain Spatiotemporal Networks With Different Numbers of Nodes

School of Physics and Electronic Technology, Liaoning Normal University, Dalian, Liaoning 116029, P.R.China

摘要

摘要: 研究了节点数不同的不确定时空网络的指数外同步问题.首先，基于Lyapunov稳定性定理，通过设计合理的控制器，实现了两个节点数不同的不确定时空网络的指数外同步.进一步确定了表示网络拓扑结构的耦合矩阵元和反馈强度的自适应律.最后，以一维Burgers系统和Logistic系统构成的时空网络为例进行了仿真模拟.结果表明，整个网络存在稳定的指数外同步现象.并且同步的速率依赖于可调参数，而网络节点数不影响整个网络同步的稳定性，说明该同步方案具有一定的普适性.
- 指数外同步 /
- 时空网络 /
- 不确定参数 /
- Lyapunov稳定性定理
Abstract: The problem of exponential outer synchronization between uncertain spatiotemporal networks with different numbers of nodes was studied. Firstly, based on the Lyapunov stability theorem, an appropriate controller was designed to realize exponential outer synchronization between uncertain spatiotemporal networks with different numbers of nodes. The adaptive law of the coupling matrix elements representing the topological structure of the network and the feedback strength was further identified. Finally, with the spatiotemporal network composed of the 1D Burgers system and the Logistic system as an example for numerical simulation. The results show that there exist stable external synchronization phenomena in the whole network. Furthermore, the synchronization speed depends on the adjustable parameters, and the number of network nodes does not affect the stability of the whole network synchronization. The proposed synchronization scheme has certain universality.
- exponential outer synchronization /
- spatiotemporal network /
- uncertain parameter /
- Lyapunov stability theorem

HTML全文

参考文献(33)

[1]	CELIKOVSKY S, LYNNYK V, CHEN G. Robust synchronization of a class of chaotic networks[J]. Journal of the Franklin Institute,2013,350(10): 2936-2948.
[2]	GAO Lixin, TONG Changfei, WANG Liyong. H_∞ dynamic output feedback consensus control for discrete-time multi-agent systems with switching topology[J]. Arabian Journal for Science & Engineering,2014,39(2): 1477-1487.
[3]	BELYKH V N, BELYKH I V, HASLERB M. Connection graph stability method for synchronized coupled chaotic systems[J]. Physica D: Nonlinear Phenomena,2004,195(1/2): 159-187.
[4]	BELYKH I V, BELYKH V N, HASLER M. Blinking model and synchronization in small-world networks with a time-varying coupling[J]. Physica D: Nonlinear Phenomena,2004,195(1/2): 188-206.
[5]	TANG Z, JU H P, LEE T H. Topology and parameters recognition of uncertain complex networks via nonidentical adaptive synchronization[J]. Nonlinear Dynamics,2016,85(4): 2171-2181.
[6]	WU Kaining, ZHAO Bingxin, YAO Yu. Synchronization of coupled neutral-type delay partial differential systems[J]. Circuits, Systems, and Signal Processing,2016,35(2): 443-458.
[7]	HAN Min, ZHANG Yamei. Complex function projective synchronization in drive-response complex-variable dynamical networks with coupling time delays[J]. Journal of the Franklin Institute,2016,353(8): 1742-1758.
[8]	PECORA L M, CARROLL T L. Master stability functions for synchronized coupled systems[J]. Physical Review Letters,1998,80(10): 2109-2112.
[9]	DHAMALA M, JIRSA V K, DING M Z. Enhancement of neural synchrony by time delay[J]. Physical Review Letters,2004,92(7): 074104.
[10]	FRASCA M, BUSCARINO A, RIZZO A, et al. Synchronization of moving chaotic agents[J]. Physical Review Letters, 2008,100(4): 044102.
[11]	PERUANI F, SIBONA G J. Dynamics and steady states in excitable mobile agent systems[J]. Physical Review Letters,2008,100(16): 168103.
[12]	WU Xuefei. Complex projective synchronization in drive-response stochastic networks with switching topology and complex-variable systems[J]. Advances in Difference Equations,2015,2015: 129. DOI: 10.1186/s13662-015-0468-9.
[13]	ZHOU Xianghui, ZHOU Wuneng, YANG Jun, et al. Stochastic synchronization of neural networks with multiple time-varying delays and Markovian jump[J]. Journal of the Franklin Institute,2015,352(3): 1265-1283.
[14]	YU Wenwu, DELELLIS P, CHEN Guanrong, et al. Distributed adaptive control of synchronization in complex networks[J]. IEEE Transactions on Automatic Control,2012,57(8): 2153-2158.
[15]	BAGHERI A, OZGOLI S. Exponentially impulsive projective and lag synchronization between uncertain complex networks[J]. Nonlinear Dynamics,2016,84(4): 2043-2055.
[16]	WANG Tianbo, ZHOU Wuneng, ZHAO Shouwei. Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach[J]. Communications in Nonlinear Science and Numerical Simulation,2013,18(8): 2097-2106.
[17]	LI Chaojie, YU Wenwu, HUANG Tingwen. Impulsive synchronization schemes of stochastic complex networks with switching topology: average time approach[J]. Neural Networks,2014,54(6): 85-94.
[18]	LIU Tao, HILL D J, ZHAO Jun. Incremental-dissipativity-based output synchronization of dynamical networks with switching topology[C]//The 53rd IEEE Annual Conference on Decision and Control (CDC 2014).Los Angeles, California, 2014.
[19]	QIU Xiang, YU Li, ZHANG Dan. Stabilization of supply networks with transportation delay and switching topology[J]. Neurocomputing,2015,155: 247-252.
[20]	LIU Jian, LIU Shutang, SPROTT J C. Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters[J]. Nonlinear Dynamics,2016,83(1/2): 1109-1121.
[21]	JIN Xiaozheng, YANG Guanghong. Adaptive sliding mode fault-tolerant control for nonlinearly chaotic systems against network faults and time-delays[J]. Journal of the Franklin Institute,2013,350(5): 1206-1220.
[22]	WANG Xiaofan, CHEN Guanrong. Synchronization in small-world dynamical networks[J]. International Journal Bifurcation and Chaos,2002,12(1): 187-192.
[23]	YANG Yongqing, CAO Jinde. Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects[J]. Nonlinear Analysis: Real World Applications,2010,11(3): 1650-1659.
[24]	WANG Lei, CHEN M Z Q, WANG Qingguo. Bounded synchronization of a heterogeneous complex switched network[J].Automatica,2015,56: 19-24.
[25]	ZHANG Chunmei, LI Wenxue, WANG Ke. Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching[J]. Nonlinear Analysis: Hybrid Systems,2015,15(3): 37-51.
[26]	WANG Lei, WANG Qingguo. Synchronization in complex networks with switching topology[J]. Physics Letters A,2011,375(34): 3070-3074.
[27]	WU Xiangjun, LU Hongtao. Generalized projective synchronization between two different general complex dynamical networks with delayed coupling[J]. Physics Letters A,2010,374(38): 3932-3941.
[28]	ALI M S, ARIK S, SARAVANAKUMAR R. Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays[J].Neurocomputing,2015,158(1): 167-173.
[29]	杜利明, 赵军. 具有切换拓扑结构的非恒等节点复杂网络同步化判据[J]. 控制理论与应用, 2013,30(5): 649-655.(DU Liming, ZHAO Jun. A synchronization criterion for dynamical networks with non-identical nodes and switching topology[J]. Control Theory & Applications,2013,30(5): 649-655.(in Chinese))
[30]	WU Yongqing, LIU Li. Exponential outer synchronization between two uncertain time-varying complex networks with nonlinear coupling[J]. Entropy,2015,17(5): 3097-3109.
[31]	闫欢, 赵振江, 宋乾坤. 具有泄漏时滞的复值神经网络的全局同步性[J]. 应用数学和力学, 2016,37(8): 832-841.(YAN Huan,ZHAO Zhenjiang, SONG Qiankun. Global synchronization of complex-valued neural networks with leakage time delays[J]. Applied Mathematics and Mechanics,2016,37(8): 832-841.(in Chinese))
[32]	张玮玮, 吴然超. 基于线性控制的分数阶混沌系统的对偶投影同步[J]. 应用数学和力学, 2016,37(7): 710-717.(ZHANG Weiwei, WU Ranchao. Dual projective synchronization of fractional-order chaotic systems with a linear controller[J]. Applied Mathematics and Mechanics,2016,37(7): 710-717.(in Chinese))
[33]	邹丽, 王振, 宗智, 等. 指数同伦法对Cauchy条件下变系数Burgers方程的解析与数值分析[J]. 应用数学和力学, 2014,35(7): 777-789.(ZOU Li, WANG Zhen, ZONG Zhi, et al. Analytical and numerical investigation of the variable coefficient Burgers equation under Cauchy condition with the exponential homotopy method[J]. Applied Mathematics and Mechanics,2014,35(7): 777-789.(in Chinese))