Clustering in diffusively coupled networks

Xia, Weiguo; Cao, Ming

doi:10.1016/j.automatica.2011.08.043

Cited by 236 publications

(170 citation statements)

References 17 publications

Supporting

Mentioning

167

Contrasting

Order By: Relevance

“…Social agents usually fail to reach consensus, but rather exhibit clustering [19] of opinions or other types of persistent disagreement. Whereas protocols, leading to consensus, have been thoroughly studied up to certain exhaustiveness, it remain a tough problem to obtain a realistic model of opinion dynamics, "complex" enough to include the possibilities of both consensus and disagreement and yet sufficiently "simple" to admit rigorous analysis.…”

Section: A Opinion Dynamics With Antagonistic Interactionsmentioning

confidence: 99%

See 1 more Smart Citation

Dichotomic differential inequalities and multi-agent coordination

Proskurnikov

Cao

2016

2016 European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

Abstract-Distributed algorithms of multi-agent coordination have attracted substantial attention from the research communities. The most investigated are Laplacian-type dynamics over time-varying weighted graphs, whose applications include, but are not limited to, the problems of consensus, opinion dynamics, aggregation and containment control, target surrounding and distributed optimization. While the algorithms solving these problems are similar, for their analysis different mathematical techniques have been used. In this paper, we propose a novel approach, allowing to prove the stability of many Laplacian-type algorithms, arising in multi-agent coordination problems, in a unified elegant way. The key idea of this approach is to consider an associated linear differential inequality with the Laplacian matrix, satisfied by some bounded outputs of the agents (e.g. the distances to the desired set in aggregation and containment control problems). Although such inequalities have many unbounded solutions, under natural connectivity conditions all their bounded solutions converge (and even reach consensus), entailing the convergence of the original protocol. The differential inequality thus admits only convergent but not "oscillatory" bounded solutions. This property, referred to as the dichotomy, has been long studied in the theory of differential equations. We show that a number of recent results from multi-agent control can be derived from the dichotomy criteria for Laplacian differential inequalities, developed in this paper, discarding also some technical restrictions.

show abstract

Section: A Opinion Dynamics With Antagonistic Interactionsmentioning

confidence: 99%

“…Another reason for disagreement and clustering in social networks is the agents heterogeneity, caused e.g. by their "stubborness" [21]: some agents are "attached" to their initial opinions and take them into account on each iteration of opinion change (such agents are also called "informed" [19]). …”

Section: A Opinion Dynamics With Antagonistic Interactionsmentioning

confidence: 99%

Dichotomic differential inequalities and multi-agent coordination

Proskurnikov

Cao

2016

2016 European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Over the past few decades, complex network systems have attracted a great deal of attention from different fields of scientific research such as the Internet networks, electricity distribution networks, and biological networks [1][2][3]. Although there have been many research results on the linear complex network systems, [4] studied how different mechanisms may lead to clustering behavior in connected networks consisting of diffusively coupled agents, [5] talked about the exponential synchronization of linear complex networks, and [6] studied the problem of MIMO networked control systems with packet disordering. However, in practical situations, linear complex network systems cannot reflect the reality of the physical systems completely; in order to solve this problem, people started to study the complex network systems which contain the nonlinear dynamics.…”

Section: Introductionmentioning

confidence: 99%

Cluster synchronization in nonlinear complex networks under sliding mode control

2015

View full text Add to dashboard Cite

This paper investigates the cluster synchronization for network of nonlinear systems via differential mean value theorem method and sliding mode control strategy. Because of the existence of the nonlinear dynamics, the differential mean value theorem method is used to transform the nonlinear error complex network system into a linear parameter-varying system. Since the robustness to the uncertainties of the sliding mode, we can deal with the linear parametervarying system which contains the time-varying mismatched uncertainties by applying the sliding mode control strategy through the equivalent transformation. In addition, appropriate linear matrix inequality stability condition by the Lyapunov method is derived such that each subsystem in the new sliding mode is completely invariant to both matched and mismatched uncertainties. Finally, simulation example is shown to illustrate the effectiveness of the proposed method.

show abstract

“…These agents have some level of "anchorage" on their initial opinions (prejudices) and factor them into any iteration of their opinions. Similar to continuous-time clustering protocols with "informed" leaders (Xia and Cao, 2011), the heterogeneity of the prejudices and its linkage to individuals' susceptibilities to interpersonal influence may lead to persistent disagreement of opinions and outcomes such as polarization and clustering. With the FJ model, the clustering of opinions does not require the existence of repulsive couplings, or "negative ties" among individuals (Fläche and Macy, 2011;Altafini, 2013;Proskurnikov et al, 2016a;Xia et al, 2016) whose ubiquity in interpersonal interactions is still waiting for supporting experimental evidence (Takács et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Opinion evolution in time-varying social influence networks with prejudiced agents

et al. 2017

Self Cite

View full text Add to dashboard Cite

Investigation of social influence dynamics requires mathematical models that are "simple" enough to admit rigorous analysis, and yet sufficiently "rich" to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin and Johnsen, 1999) to take into account individuals' ongoing attachments to their initial opinions, or prejudices. The "anchorage" of individuals to their prejudices may disable reaching consensus and cause disagreement in a social influence network. Further elaboration of this model may be achieved by relaxing its restrictive assumption of a time-invariant influence network. During opinion dynamics on an issue, arcs of interpersonal influence may be added or subtracted from the network, and the influence weights assigned by an individual to his/her neighbors may alter. In this paper, we establish new important properties of the (Friedkin and Johnsen, 1999) opinion formation model, and also examine its extension to time-varying social influence networks.

show abstract

Clustering in diffusively coupled networks

Cited by 236 publications

References 17 publications

Dichotomic differential inequalities and multi-agent coordination

Dichotomic differential inequalities and multi-agent coordination

Cluster synchronization in nonlinear complex networks under sliding mode control

Opinion evolution in time-varying social influence networks with prejudiced agents

Contact Info

Product

Resources

About