Liu Xiwei, Chen Tianping
Key Laboratory of Embedded System and Service Computing, Ministry of Education, Department of Computer Science and Technology, Tongji University, Shanghai, China.
IEEE Trans Neural Netw. 2011 Jul;22(7):1009-20. doi: 10.1109/TNN.2011.2139224. Epub 2011 May 16.
In this paper, we investigate the cluster synchronization problem for linearly coupled networks, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, etc., by adding some simple intermittent pinning controls. We assume the nodes in the network to be identical and the coupling matrix to be asymmetric. Some sufficient conditions to guarantee global cluster synchronization are presented. Furthermore, a centralized adaptive intermittent control is introduced and theoretical analysis is provided. Then, by applying the adaptive approach on the diagonal submatrices of the asymmetric coupling matrix, we also get the corresponding cluster synchronization result. Finally, numerical simulations are given to verify the theoretical results.
在本文中，我们通过添加一些简单的间歇牵制控制，研究线性耦合网络的簇同步问题，这些线性耦合网络可以是递归连接神经网络、细胞神经网络、霍奇金 - 赫胥黎模型、洛伦兹混沌振子等。我们假设网络中的节点是相同的，并且耦合矩阵是不对称的。给出了一些保证全局簇同步的充分条件。此外，引入了一种集中式自适应间歇控制并进行了理论分析。然后，通过将自适应方法应用于不对称耦合矩阵的对角子矩阵，我们也得到了相应的簇同步结果。最后，给出了数值模拟以验证理论结果。
