New approach to synchronization analysis of linearly coupled ordinary differential systems

By Wenlian Lu, Tianping Chen. 2006

622 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9e7899be09f0e1ebab4e33b7ddae7776214b3b07

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. Z. Duan
6. Tianping Chen
7. Zidong Wang
8. Huijun Gao

In Statistical and Nonlinear Physics

1. Jinde Cao
2. Wenwu Yu
3. Guanrong Chen
4. Jürgen Kurths
5. Tianping Chen
6. Xiwei Liu
7. Jianquan Lu
8. Wenlian Lu

Citations in the corpus

• Consensus of multi-agent systems with intrinsic nonlinear dynamics and sampled-data information (2011, background): “Lemma 1: [28], [29] Suppose that a directed graph G(A) is strongly connected.”
• Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control (2016, background): “Remark 1 Most of the researches on synchronization of dynamical network have been performed under some implicit assumptions that there exists the information communication of nodes only at time t [5] or at time t − τ [21].”
• A Distributed Dynamic Event-Triggered Control Approach to Consensus of Linear Multiagent Systems With Directed Networks (2020, background): “Lemma 2 [34]: Under Assumption 2, there exists a vector ξ = [ξ1, ξ2, .”
• Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint (2016, methodology): “For the model (5) with directed coupling, a nonorthogonal projection of x(t) on the synchronization manifold S,̄ X(t) = [x̄(t), · · · , x̄(t)] , where x̄(t) = ∑N i=1 ξixi(t), was first introduced in [2].”
• Boundedness and synchronization of y-coupled Lorenz systems with or without controllers ☆ (2008, neutral): “Define a reference trajectory (see [30])”
• Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability (2020, background): “Definition 1 [31], [32]: For the network (1), the set S = {( z1 (t), .”
• Finite-time stochastic synchronization of complex networks (2010, background): “Several approaches have been proposed for the chaos synchronization of complex dynamical networks without control [10–14].”
• Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings (2013, methodology): “Together with Assumption 1 [53], the algorithm is formulated as follows: where and Δ m > 0 .”
• Global synchronization and asymptotic stability of complex dynamical networks (2006, background): “The objective is to find a condition satisfied by the coupling matrix under which the solutions of network (1) globally asymptotically synchronize each other, in the sense that for all (4) Next, following [13], let , , , and .”
• Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics (2010, background): “This scenario arises naturally when agents have intrinsic nonlinear dynamics [4], [17], [18], [21], [29]–[32], [34], [35], [38], [42], [43].”
• Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances (2011, background): “described by the following delayed differential equations [19], [34]: ẋi (t) = Cxi (t) + B1 f (xi (t)) + B2 f (xi (t − τ (t))) + I (t)”
• Pinning Complex Networks by a Single Controller (2006, neutral): “In the paper [5], based on the geometric structure of the synchronization manifold, a thorough theoretical analysis of the synchronization of LCODEs is given.”
• Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control (2015, background): “Definition 1: (See [6], [9]) Matrix A = (ajk)j,k=1 is said to belong to class A1, denoted as A ∈ A1, if A is irreducible, and ajk ≥ 0, j = k, ajj = − ∑N k=1,k =j ajk, j = 1, · · · , N .”
• Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay (2006, methodology): “Furthermore, we extend the methodology introduced in [17] to the delayed coupled systems.”
• Cluster Synchronization in Directed Networks Via Intermittent Pinning Control (2011, neutral): “Similar definitions have been widely adopted in the synchronization literature, [15], [16], [18].”
• Consensus in Directed Networks of Agents With Nonlinear Dynamics (2011, neutral): “[16] T.”