Emergent behavior in large scale networks

Santos, Augusto; Moura, J.M.F.

doi:10.1109/cdc.2011.6161398

Cited by 13 publications

(9 citation statements)

References 16 publications

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“…The ODE (13)- (14) also describes the dynamics of diffusion of two strains of virus in a self-linked singlenode e-network and it was studied in Reference [23], from where the asymptotics follows.…”

Section: General E-network: Bi-virusmentioning

confidence: 99%

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Santos

Moura

2015

IEEE Trans. Netw. Sci. Eng.

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Abstract-The paper studies the qualitative behavior of a set of Ordinary Differential Equations that models the dynamics of bi-virus epidemics over bilayer networks. Each layer is a weighted digraph associated with a strain of virus; the weights γ z ij represent the rates of infection from node i to node j of strain z. We establish a sufficient condition on the γ's that guarantees survival of the fittest-only one strain survives. We propose an ordering of the weighted digraphs, the -order, and show that if the weighted digraph of strain y is -dominated by the weighted digraph of strain x, then y dies out in the long run. We prove that the orbits of the ODE accumulate to an attractor. Due to the coupled nonlinear high-dimension nature of the ODEs, there is no natural Lyapunov function to study their global qualitative behavior. We prove our results by combining two important properties of these ODEs: (i) monotonicity under a partial ordering on the set of graphs; and (ii) dimension-reduction under symmetry of the graphs. Property (ii) allows us to fully address the survival of the fittest for regular graphs. Then, by bounding the epidemics dynamics for generic networks by the dynamics on regular networks, we prove the result for general networks.

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Section: General E-network: Bi-virusmentioning

confidence: 99%

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Santos

Moura

2015

IEEE Trans. Netw. Sci. Eng.

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“…Proof: In order to prove ergodicity, it is convenient to use the additive noise model representation in (16), which we report here for convenience:…”

Section: Appendix B Proof Of Propositionmentioning

confidence: 99%

Topology Inference over Networks with Nonlinear Coupling

Santos¹,

Matta²,

Sayed³

2019

Preprint

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This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution. The dynamical law governing the state-evolution of the interacting agents might be nonlinear, i.e., the next state of an agent can depend nonlinearly on its current state and on the states of its immediate neighbors. We establish sufficient conditions that allow consistent graph learning over a special class of networked systems, namely, logistic-type dynamical systems.

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“…In the contact process, a healthy agent can only become infected through contagion from an infected neighbor. It may be the case that a healthy agent (or working component) may also become infected (or fail) due to an exogenous (i.e., outside of the network) source -the agent is infected spontaneously [15], [1], [16]. For SIS epidemics, this is captured by a non-zero exogenous infection rate, λ.…”

Section: A Extended Contact Processmentioning

confidence: 99%

Contact process with exogenous infection and the scaled SIS process

Zhang

Moura²

2017

Journal of Complex Networks

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Propagation of contagion in networks depends on the graph topology. This article is concerned with studying the time-asymptotic behaviour of the extended contact processes on static, undirected, finite-size networks. This is a contact process with nonzero exogenous infection rate (also known as the $\epsilon$-susceptible-infected-susceptible model). The only known analytical characterization of the equilibrium distribution of this process is for complete networks. For large networks with arbitrary topology, it is infeasible to numerically solve for the equilibrium distribution since it requires solving the eigenvalue-eigenvector problem of a matrix that is exponential in $N$, the size of the network. We derive a condition on the infection rates under which, depending on the degree distribution of the network, the equilibrium distribution of extended contact processes on arbitrary, finite-size networks is well approximated by a closed-form formulation. We confirm the goodness of the approximation with small networks answering inference questions like the distribution of the percentage of infected individuals and the most-probable equilibrium configuration. We then use the approximation to analyse the equilibrium distribution of the extended contact process on the 4941-node US Western power grid.

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Emergent behavior in large scale networks

Cited by 13 publications

References 16 publications

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Bi-Virus SIS Epidemics over Networks: Qualitative Analysis

Topology Inference over Networks with Nonlinear Coupling

Contact process with exogenous infection and the scaled SIS process

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