Modulus synchronization in a network of nonlinear systems with antagonistic interactions and switching topologies

Zhai, Shidong

doi:10.1016/j.cnsns.2015.09.010

Cited by 32 publications

(18 citation statements)

References 22 publications

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“…The aim of this article is only to investigate whether or not the deviations between modular outputs vanish, while the outputs themselves may or may not converge to a static equilibrium vector. Consequently, we use the term "modulus/bipartite synchronization" in Definition 1 by extending the relevant concepts of multi-agent cooperative control with antagonistic interaction [26], [27]. It is different from the usual modulus/bipartite consensus definition introduced in [16], [20], in which the outputs or rather states of all social actors are required to converge in modulus to a constant.…”

Section: Problem Formulation and Elementary Resultsmentioning

confidence: 99%

Opinion Behavior Analysis in Social Networks Under the Influence of Coopetitive Media

Xue

Hirche

Cao

2020

IEEE Trans. Netw. Sci. Eng.

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Both interpersonal communication and media contact are important information sources and play a significant role in shaping public opinions of large populations. In this article, we investigate how the opinion-forming process evolves over social networks under the media influence. In addition to being affected by the opinions of their connected peers, the media cooperate and/or compete mutually with each other. Networks with mixed cooperative and competitive interactions are said to be coopetitive. In this endeavor, a novel mathematical model of opinion dynamics is introduced, which captures the information diffusion process under consideration, makes use of the community-based network structure, and takes into account personalized biases among individuals in social networks. By employing port-Hamiltonian system theory to analyze the modeled opinion dynamics, we predict how public opinions evolve in the long run through social entities and find applications in political strategy science. A key technical observation is that as a result of the port-Hamiltonian formulation, the mathematical passivity property of individuals' self-dynamics facilitates the convergence analysis of opinion evolution. We explain how to steer public opinions towards consensus, polarity, or neutrality, and investigate how an autocratic media coalition might emerge regardless of public views. We also assess the role of interpersonal communication and media exposure, which in itself is an essential topic in mathematical sociology.

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Section: Problem Formulation and Elementary Resultsmentioning

confidence: 99%

Opinion Behavior Analysis in Social Networks Under the Influence of Coopetitive Media

Xue

Hirche

Cao

2020

IEEE Trans. Netw. Sci. Eng.

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“…Note that the signed networks in most of current works [25][26][27][28][29][30][31][32][33] are assumed to be composed by identical linear systems. In recent years, some attention has been paid to the coordination control of signed networks with nonlinear dynamics: Hu et al 47 considered the traditional synchronization problem for signed networks with Lipschitz-type node dynamics; Zhai et al [48][49][50] studied the bipartite leaderless and leader-following synchronization in a network of nonlinear systems satisfying the one-sided Lipschitz condition. Since nonlinear systems exhibit rich and complex dynamics, the nodes of nonlinear signed networks may satisfy other kinds of conditions such as the well-known sector condition, [34][35][36][37][38] whose coordination control deserves to be deeply investigated.…”

Section: Main Motivationsmentioning

confidence: 99%

“…Therefore, compared with the continuous‐time control algorithms, the sampled‐data control algorithms can significantly reduce the communication load of the signed Lur'e networks. Noting that the bipartite synchronization algorithms for nonlinear signed networks in the current literature are usually designed in continuous‐time setting, this paper presents both continuous‐time and sampled‐data control algorithms. Different from the continuous‐time control algorithms for unsigned Lur'e networks, the proposed continuous‐time control algorithms for reaching bipartite synchronization in signed Lur'e networks need to consider both the network structure and node dynamics.…”

Section: Introductionmentioning

confidence: 99%

Bipartite synchronization of Lur'e network under signed digraph

Liu

Song

Wen

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper considers the bipartite leaderless and leader‐following synchronization in a network of coupled Lur'e systems with sector‐condition node dynamics and signed digraph topology, where the interaction digraph consists of both positive and negative communication links. Continuous‐time and sampled‐data control algorithms are, respectively, proposed to solve the bipartite synchronization problems for the signed Lur'e network. Under some assumptions on the network structure and node functions, some bipartite synchronization conditions are established for signed Lur'e network by using coordinate transform, linear matrix inequalities, and algebraic graph theories. For the continuous‐time control algorithms, it is shown that the bipartite synchronization problems of the signed Lur'e network can always be solved if the coupling strength is sufficiently large and the network topology satisfies some suitable conditions. For the sampled‐data control algorithms, an upper bound of the sampling intervals is estimated to ensure that the bipartite synchronization can be reached in the signed Lur'e network. Some simulation results are given to illustrate the effectiveness of the theoretical analysis.

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“…Lou and Hong 18 extended the results in the work of Altafini 6 by assuming signed networks have complex-value weights and obtained a uniform condition to ensure consensus and bipartite consensus. Zhai 19 considered a bipartite consensus control for first-order nonlinear multiagent systems with switching networks by using contraction theory. For cooperative-competitive multiagent systems with high-order agent dynamics, a static state-feedback controller was proposed in the work of Valcher and Misra, 7 and a dynamic output feedback controller was given in the work of Zhang and Chen 20 to guarantee bipartite consensus.…”

Section: Introductionmentioning

confidence: 99%

Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks

Liu

et al. 2018

Intl J Robust & Nonlinear

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In this paper, a bipartite consensus problem is considered for a high-order multiagent system with cooperative-competitive interactions and unknown time-varying disturbances. A signed graph is used to describe the interaction network associated with the multiagent system. The unknown disturbances are expressed by linearly parameterized models, and distributed adaptive laws are designed to estimate the unknown parameters in the models. For the case that there is no exogenous reference system, a fully distributed adaptive control law is proposed to ensure that all the agents reach a bipartite consensus. For the other case that there exists an exogenous reference system, another fully distributed adaptive control law is also developed to ensure that all the agents achieve bipartite consensus on the state of the exogenous system. The stability of the closed-loop multiagent systems with the 2 proposed adaptive control laws are analyzed under an assumption that the interaction network is structurally balanced. Moreover, the convergence of the parameter estimation errors is guaranteed with a persistent excitation condition. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed adaptive bipartite consensus control laws for the concerned multiagent system. KEYWORDSbipartite consensus, coopetition networks, distributed adaptive control, high-order multiagent systems 2868

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Modulus synchronization in a network of nonlinear systems with antagonistic interactions and switching topologies

Cited by 32 publications

References 22 publications

Opinion Behavior Analysis in Social Networks Under the Influence of Coopetitive Media

Opinion Behavior Analysis in Social Networks Under the Influence of Coopetitive Media

Bipartite synchronization of Lur'e network under signed digraph

Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks

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