将Rossler混沌系统作为神经元，先建立星形子网络，再将子网络的中心神经元按照完全连接形式连接，构建复合型网络. 采用并扩展使2个混沌系统同步的稳定性准则(SC)同步方法，对所构建的复合型网络的同步控制进行理论研究与数值模拟分析.提出了复合型网络的系统耦合方程，以及网络中神经元之间的同步误差发展方程.通过对相关耦合强度因子的控制，将参数对网络同步的形式与过程的影响进行了详细的讨论，得到了复合型网络中可能存在的混沌同步类型与相对应的参数控制范围，并证明了SC同步方法可以有效地解决由星形和完全连接型子网络构成的复合型网络的混沌同步问题.
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.
［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.
