Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control.
Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control.
复制标题
通过间歇控制的混合耦合定向延迟动态网络的钉扎同步。
作者：
Shuiming Cai;Peipei Zhou;Zengrong Liu
本文研究了一类具有混合耦合的一般时滞动态网络的指数同步问题。该网络模型同时考虑了内部时延和耦合时延。同时，在延迟耦合项中考虑了传输时延和自反馈时延。通过建立一个新的微分不等式，解析地得到了几个简单实用的指数同步判据。结果表明，与传统的同步解相比，受控同步状态是可以改变的，节点的阶数和内部延迟耦合矩阵对受控同步状态有重要影响。通过选择不同的内部延迟耦合矩阵和节点的阶数，可以得到不同的受控同步状态。此外，还给出了细节钉扎方案，该方案决定了应选择哪些节点作为钉扎候选节点，以及固定耦合强度需要钉扎多少节点。给出了在实际应用中如何设计合适的间歇控制器的简单步骤。最后给出了无向无标度网络和有向小世界网络的数值模拟结果，验证了理论结果的有效性。
This paper concerns the problem of exponential synchronization for a class of general delayed dynamical networks with hybrid coupling via pinning periodically intermittent control. Both the internal delay and coupling delay are taken into account in the network model. Meanwhile, the transmission delay and self-feedback delay are involved in the delayed coupling term. By establishing a new differential inequality, several simple and useful exponential synchronization criteria are derived analytically. It is shown that the controlled synchronization state can vary in comparison with the conventional synchronized solution, and the degree of the node and the inner delayed coupling matrix play important roles in the controlled synchronization state. By choosing different inner delayed coupling matrices and the degrees of the node, different controlled synchronization states can be obtained. Furthermore, the detail pinning schemes deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength are provided. The simple procedures illuminating how to design suitable intermittent controllers in real application are also given. Numerical simulations, including an undirected scale-free network and a directed small-world network, are finally presented to demonstrate the effectiveness of the theoretical results.
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