666 research outputs found
Clustering in diffusively coupled networks
This paper shows how different mechanisms may lead to clustering behavior in connected networks consisting of diffusively coupled agents. In contrast to the widely studied synchronization processes, in which the states of all the coupled agents converge to the same value asymptotically, in the cluster synchronization problem studied in this paper, we require all the interconnected agents to evolve into several clusters and each agent only to synchronize within its cluster. The first mechanism is that agents have different self-dynamics, and those agents having the same self-dynamics may evolve into the same cluster. When the agents' self-dynamics are identical, we present two other mechanisms under which cluster synchronization might be achieved. One is the presence of delays and the other is the existence of both positive and negative couplings between the agents. Some sufficient and/or necessary conditions are constructed to guarantee n-cluster synchronization. Simulation results are presented to illustrate the effectiveness of the theoretical analysis. (C) 2011 Elsevier Ltd. All rights reserved
Diffusion-induced instability and chaos in random oscillator networks
We demonstrate that diffusively coupled limit-cycle oscillators on random
networks can exhibit various complex dynamical patterns. Reducing the system to
a network analog of the complex Ginzburg-Landau equation, we argue that uniform
oscillations can be linearly unstable with respect to spontaneous phase
modulations due to diffusional coupling - the effect corresponding to the
Benjamin-Feir instability in continuous media. Numerical investigations under
this instability in random scale-free networks reveal a wealth of complex
dynamical regimes, including partial amplitude death, clustering, and chaos. A
dynamic mean-field theory explaining different kinds of nonlinear dynamics is
constructed.Comment: 6 pages, 3 figure
Symmetry-Induced Clustering in Multi-Agent Systems using Network Optimization and Passivity
This work studies the effects of a weak notion of symmetry on
diffusively-coupled multi-agent systems. We focus on networks comprised of
agents and controllers which are maximally equilibrium independent passive, and
show that these converge to a clustered steady-state, with clusters
corresponding to certain symmetries of the system. Namely, clusters are
computed using the notion of the exchangeability graph. We then discuss
homogeneous networks and the cluster synthesis problem, namely finding a graph
and homogeneous controllers forcing the agents to cluster at prescribed values.Comment: 7 pages, 4 figure
Conedy: a scientific tool to investigate Complex Network Dynamics
We present Conedy, a performant scientific tool to numerically investigate
dynamics on complex networks. Conedy allows to create networks and provides
automatic code generation and compilation to ensure performant treatment of
arbitrary node dynamics. Conedy can be interfaced via an internal script
interpreter or via a Python module
Cluster Assignment in Multi-Agent Systems : Sparsity Bounds and Fault Tolerance
We study cluster assignment in homogeneous diffusive multi-agent networks.
Given the number of clusters and agents within each cluster, we design the
network graph ensuring the system will converge to the prescribed cluster
configuration. Using recent results linking clustering and symmetries, we show
that it is possible to design an oriented graph for which the action of the
automorphism group of the graph has orbits of predetermined sizes, guaranteeing
the network will converge to the prescribed cluster configuration. We provide
bounds on the number of edges needed to construct these graphs along with a
constructive approach for their generation. We also consider the robustness of
the clustering process under agent malfunction.Comment: 12 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2203.0664
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