IEEE Trans Nanobioscience. 2017 Oct;16(7):585-599. doi: 10.1109/TNB.2017.2738324. Epub 2017 Aug 10.
In this paper, we study the cluster synchronization of coupled genetic regulatory networks with time-varying delays via aperiodically adaptive intermittent control on some nodes. The network is intermittently coupled and the intra-cluster coupling strength is adaptively adjusted. The graph of the coupling topology of each cluster is only required to have a directed spanning tree. Two cases of delays are considered. In the first case, by using the switching Lyapunov-based function and Razumikhin-type technique, the cluster synchronization criterion is presented which indicates that the cluster synchronization is realized via the aperiodically adaptive intermittent control. The second case is investigated by using the switching Lyapunov functional. Both the cluster synchronization criteria are established by the Linear Matrix Inequalities (LMIs), the lower bound of the aperiodical time span, and the maximum uncontrolled ratio. It is shown that the results are applicable to both the situations that the upper bound of the delay is larger and smaller than the lower bound of the aperiodical coupling and control width. Numerical simulations are carried out to illustrate the theoretical results.
在本文中，我们通过在某些节点上进行非周期性自适应间歇控制，研究了具有时变时滞的耦合遗传调控网络的簇同步。网络是间歇耦合的，并且簇内耦合强度是自适应调整的。每个簇的耦合拓扑图只需要有一个有向生成树。考虑了两种延迟情况。在第一种情况下，通过使用切换 Lyapunov 基函数和 Razumikhin 型技术，提出了簇同步准则，表明通过非周期性自适应间歇控制实现了簇同步。第二种情况通过切换 Lyapunov 泛函进行研究。簇同步准则均通过线性矩阵不等式（LMIs）、非周期性时跨度的下界和最大无控制比建立。结果表明，这些结果适用于延迟的上界大于和小于非周期性耦合和控制宽度的下界的两种情况。通过数值模拟验证了理论结果。
