The Rossler chaotic system is considered as neurons,a sub network of star-shaped is firstly established. Then a composite large network is constructed by connecting the center neuron of the sub network with all-to-all-coupling connection. Using and extending the stability criterion (SC)synchronization method of two chaotic systems, theoretical research and numerical simulation are carried out for the constructed network. The system coupled equations of the network and the synchronization error development equations between the neurons in the network are provided. By controlling the dependent coupling intensity factor, the influence of parameters on network synchronization form and process are discussed in detail, and the possible chaos synchronization types and the ranges of the controlled parameter are obtained. Also, it is proved that the SC synchronization method is effectively useful to solve the chaotic synchronization problem of the composite network composed of the star-shaped and all-to-all-coupling.
YU Hongjie,DONG Yixuan
. Synchronization of the Composite Network Constructed by
the R?ssler Chaotic System[J]. Journal of Shanghai Jiaotong University, 2018
, 52(12)
: 1559
-1564
.
DOI: 10.16183/j.cnki.jsjtu.2018.12.003
[1]OTT E, GREBOGI C, YORKE J A. Controlling chaos[J]. Physical Review Letters, 1990, 64(11): 1196-1199.
[2]PECORA L M, CARROLL T L. Synchronization in chaos systems[J]. Physical Review Letters, 1990, 64(8): 821-824.
[3]PECORA L M, CARROLL T L. Synchronization of chaotic systems[J]. Chaos An Interdisciplinary Journal of Nonlinear Science, 2015, 25(9): 2891-5100.
[4]AL-SAWALHA M M, SHOAIB M. Adaptive modified synchronization of hyperchaotic systems with fully unknown parameters[J]. International Journal of Dynamics and Control, 2016, 4(1): 23-30.
[5]任涛, 朱志良, 于海, 等. 基于Min-Max方法的混沌系统采样同步控制研究[J]. 物理学报, 2013, 62(17): 170501.
REN Tao, ZHU Zhiliang, YU Hai, et al. The study on sampling synchronization control of chaotic system based on Min-Max method[J]. Acta Physica Sinica, 2013, 62(17): 170501.
[6]REZA B, MOHAMMADALI B. Optimal synchronization of two different in-commensurate fractional-order chaotic systems with fractional cost function[J]. Complexity, 2016(S1): 401-416.
[7]KHADRA F A. Synchronization of chaotic systems via active disturbance rejection control[J]. Intelligent Control and Automation, 2017, 8(2): 86-95.
[8]ROSIN D P, RONTANI D, GAUTHIER D J, et al. Control of synchronization patterns in neural-like Boolean networks[J]. Physical Review Letters, 2013, 110(10): 104102.
[9]钟超林, 李国刚. 一种基于混沌神经网络的安全组播通信方法[J]. 武汉大学学报(工学版), 2016, 49(4): 635-640.
ZHONG Chaolin, LI Guogang. Secure multicast communication method based on chaotic neural network[J]. Engineering Journal of Wuhan University, 2016, 49(4): 635-640.
[10]PECORA L M, SORRENTINO F, HAGERSTROM A M, et al. Cluster synchronization and isolated desynchronization in complex networks with symmetries[J]. Nature Communications, 2014, 5(4079): 1-8.
[11]SORRENTINO F, PECORA L M, HAGERSTROM A M, et al. Complete characterization of the stability of cluster synchronization in complex dynamical networks[J]. Science Advances, 2016, 2(4): e1501737.
[12]DUAN L, HUANG L H, FANG X W. Finite-time synchronization for recurrent neural networks with discontinuous activations and time-varying delays[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017, 27(1): 013101-10.
[13]YU H J, LIU Y Z. Chaotic synchronization based on stability criterion of linear systems[J]. Physics Letters A, 2003, 314(4): 292-298.
[14]于洪洁, 郑宁. 非线性函数耦合的Chen吸引子网络的混沌同步[J]. 物理学报, 2008, 57(8): 4712-4720.
YU Hongjie, ZHENG Ning. Chaotic synchronization of network of Chen’s chaotic attractors using nonlinear coupling function[J]. Acta Physica Sinica, 2008, 57(8): 4712-4720.
[15]张文龙, 于洪洁. 一种星形神经网络的混沌同步[J]. 上海交通大学学报, 2013, 47(2): 220-225.
ZHANG Wenlong, YU Hongjie. Chaotic synchronization of a type of star-shaped neural network[J]. Journal of Shanghai Jiao Tong University, 2013, 47(2): 220-225.