Synchronization in networks of nonlinear dynamical systems coupled via a directed graph

By Chai Wah Wu. 2005

290 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/745b9ef83d9958b009c8b57c9012d1abb1a28f77

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Guanrong Chen
2. Wenwu Yu
3. Jinde Cao
4. Jürgen Kurths
5. Wei Ren
6. Z. Duan
7. Jinhu Lu
8. Zhongkui Li

In Molecular Biology

1. Wenwu Yu
2. Guanrong Chen
3. Jinde Cao
4. Jürgen Kurths
5. Jinhu Lu
6. Ming Cao
7. Jianquan Lu
8. Wei Ren

Citations in the corpus

• Cluster Synchronization in Directed Networks Via Intermittent Pinning Control (2011, unknown): “Similar definitions have been widely adopted in the synchronization literature, [15], [16], [18].”
• Distributed Consensus of Second-Order Multi-Agent Systems With Heterogeneous Unknown Inertias and Control Gains Under a Directed Graph (2016, background): “Therefore, the results available in [28] and [17] cease to be applicable in our problem.”
• Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint (2016, background): “Lemma 3: If graph contains a directed spanning tree, then, with proper permutation, can be reduced to the Frobenius normal form [41]”
• Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay (2006, background): “Remark 4 It can be seen (see [15]) that ΛA + AΛ is negative definite in the subspace L since A ∈ A2.”
• Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics (2010, background): “Some useful concepts have been proposed in [31].”
• Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances (2011, methodology): “By referring to the concept of β(A) in Definition 4, the results in Theorem 2 and techniques in [11], the results can be extended to the case of reducible coupling (containing rooted spanning tree [37]), which means that the network is not required to be strongly connected.”
• Consensus of multi‐agent systems with nonlinear dynamics and sampled‐data information: a delayed‐input approach (2013, background): “Pertinent works along this line include [27–29], where consensus problem of continuous-time coupled systems are investigated.”
• Conditions for Synchronizability in Arrays of Coupled Linear Systems (2008, background): “When the set is the collection of all interconnections with coupling strength greater than some (a priori known) positive threshold, the answer (which can be extracted, for instance, from [32]) is as simple as one can expect: that (C, A) is detectable, just as is the case with Luenberger observer.”
• LQR-based coupling gain for synchronization of linear systems (2008, background): “In [28] an equivalent condition (for connectedness) is given as that the graph contains a spanning tree.”
• Consensus in Directed Networks of Agents With Nonlinear Dynamics (2011, background): “Lemma 8: Suppose that the Laplacian matrix is irreducible.”