Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller
Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller
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DOI：
10.1002/asjc.2053
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发表时间：
2019-02
影响因子：
2.4
通讯作者：
Lili Zhang;Yinhe Wang;Qingyun Wang;S. Qiao;F. Wang
中科院分区：
文献类型：
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作者：
Lili Zhang;Yinhe Wang;Qingyun Wang;S. Qiao;F. Wang
研究了复杂动态网络中节点间的广义投影同步问题。我们的网络模型同时考虑了现实网络的多种特性。首先，在我们的CDN中引入一个关键节点，它表现得像一个领导者，存在于许多实际网络中。其次，讨论了关键节点与其他节点之间的共性，并将其体现在网络模型中。第三，我们的CDN由不同维度的节点组成，具有整体时变耦合强度。为了描述更多的同步现象，定义了指数广义投影同步（EGPS）和渐近广义投影同步（AGPS）。本文的主要目标是设计一个有效的，但简单的分散控制器的关键节点，使我们的网络实现GPS。在严格理论推导的基础上，根据总体耦合强度是确定的还是自适应的，分别提出了EGPS和AGPS方案。以前很少有研究关注这一点。值得指出的是，本文中的控制输入和耦合强度自适应律都只存在于关键节点的信息中，这在一定程度上暗示了关键节点的重要性。最后，通过两个数值仿真算例验证了理论结果的有效性和可行性.
This paper investigates the generalized projective synchronization (GPS) among the nodes within a complex dynamical network (CDN). Multiple characteristics of realistic networks are simultaneously considered in our network model. First, one crucial node is introduced into our CDN, which behaves like a leader and exists in many practical networks. Second, the commonalities between the crucial node and every other node are discussed and they are embodied in the network model. Third, our CDN is composed of different dimensional nodes and has an overall time‐varying coupling strength. Furthermore, in order to describe more synchronous phenomena, the exponential generalized projective synchronization (EGPS) and asymptotic generalized projective synchronization (AGPS) are defined. The main objective of this paper is to design an effective but simple decentralized controller for the crucial node such that our network realizes GPS. Based on rigorous theoretical derivations, EGPS and AGPS schemes are respectively proposed according to whether the overall coupling strength is certain or adaptive. Few previous studies have focused on this. It is worth pointing out that both the control input and the adaptive law of the coupling strength in this paper only lie in the information of the crucial node, which implies the significance of the crucial node to some extent. Finally, the effectiveness and feasibility of our theoretical results are verified by two numerical simulation examples.