Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

Leiser, Randolph J.; Rotstein, Horacio G.

doi:10.1103/physreve.96.022303

Cited by 2 publications

(1 citation statement)

References 120 publications

(117 reference statements)

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“…Each cluster might contains smaller clusters inside, resulting in a hierarchical and multi-layer clustered network. This type of system can be found in a variety of application domains including energy systems [1], robotics [2], biological and chemical engineering [3], [4], social networks [5], brain science [6], epidemic [7], etc., and has been a timely research topic in network science [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Distributed two-time-scale methods over clustered networks

Pham,

Doan,

Nguyen

2020

Preprint

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In this paper, we consider consensus problems over a network of nodes, where the network is divided into a number of clusters. We are interested in the case where the communication topology within each cluster is dense as compared to the sparse communication across the clusters. Moreover, each cluster has one leader which can communicate with other leaders in different clusters. The goal of the nodes is to agree at some common value under the presence of communication delays across the clusters.Our main contribution is to propose a novel distributed twotime-scale consensus algorithm, which pertains to the separation in network topology of clustered networks. In particular, one scale is to model the dynamic of the agents in each cluster, which is much faster (due to the dense communication) than the scale describing the slowly aggregated evolution between the clusters (due to the sparse communication). We prove the convergence of the proposed method in the presence of uniform, but possibly arbitrarily large, communication delays between the leaders. In addition, we provided an explicit formula for the convergence rate of such algorithm, which characterizes the impact of delays and the network topology. Our results shows that after a transient time characterized by the topology of each cluster, the convergence of the two-time-scale consensus method only depends on the connectivity of the leaders. Finally, we validate our theoretical results by a number of numerical simulations on different clustered networks.

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Section: Introductionmentioning

confidence: 99%

Distributed two-time-scale methods over clustered networks

Pham,

Doan,

Nguyen

2020

Preprint

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Periodic Orbits and Chaos in Nonsmooth Delay Differential Equations

Bel

Cobiaga

Reartes

2019

Int. J. Bifurcation Chaos

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In this paper, we present a method to find periodic solutions for certain types of nonsmooth differential equations or nonsmooth delay differential equations. We apply the method to three examples, the first is a second-order differential equation with a nonsmooth term, in this case the method allows us to find periodic orbits in a nonlinear center. The two remaining examples are first-order nonsmooth delay differential equations. In the first one, there is a stable periodic solution and in the second, the presence of a chaotic attractor was detected. In the latter, the method allows us to obtain unstable periodic orbits within the attractor. For large values of the delay, both examples can be seen as singularly perturbed delay differential equations. For them, an analysis is performed with an associated discrete map which is obtained in the limit of large delays.

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Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

Cited by 2 publications

References 120 publications

Distributed two-time-scale methods over clustered networks

Distributed two-time-scale methods over clustered networks

Periodic Orbits and Chaos in Nonsmooth Delay Differential Equations

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