Synchronization control of large-scale nonlinear network systems with delay couplings including topological design

对于具有时滞耦合的全同非线性耦合大系统网络的同步问题，我们得到了如下结果：1。我们展示了如何利用标度性质来估计网络中完全同步和部分同步的条件。我们还提出了如何设计网络结构，使网络是完全同步的。2.对于同步模式的形成问题，我们阐明了什么样的同步模式可以通过施加外部输入出现。该结果表明，同步模式可以由外部输入控制。3.本文给出了具有时滞耦合的笛卡尔积网络的完全同步和部分同步的条件。此外，对于用有向图表示的网络系统，我们提出了一种分析同步模式的图论方法和一种基于同步的系统约简方法。

For the synchronization problem in large-scale networks of identical nonlinear coupled systems with delay couplings, we obtained the following results:1. We showed how to estimate conditions for full synchronization and partial synchronization in networks by using the scaling property. We also proposed how to design a network structure such that the network is completely synchronized. 2. For the synchronization pattern formation problem, we clarified what synchronization pattern can be emerged by applying external inputs. This result indicates that the synchronization pattern can be controlled by external inputs. 3. We derived conditions for full synchronization and partial synchronization in the Cartesian product networks with delay couplings. In addition, for network systems represented by directed graphs, we proposed a graph theoretic approach for analysis of synchronization patterns and a system reduction method based on synchronization.