Uncertainty Quantification of Multi-Scale Resilience in Nonlinear Complex Networks using Arbitrary Polynomial Chaos

Zou, Mengbang; Fragonara, Luca Zanotti; Guo, Weisi

doi:10.48550/arxiv.2009.08243

Cited by 2 publications

(3 citation statements)

References 26 publications

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“…We set the initial value 0.98 < l i (t 0 ) < 1.02, the dynamic process of each node is shown in Fig. (7) (a). We can see that all nodes in this system finally converge to the quilibrium l i = 1.…”

Section: Numerical Simulation and Resultsmentioning

confidence: 99%

“…Against this background, endless load balancing should be avoided in complex system. 1.1.1 Review on Near Equilibrium Methods Recent breakthroughs have developed the framework to analyze the relationship between microscopic (like local component dynamics), macroscopic (global dynamics) behaviors and network topology [4][5][6][7]. Our previous work in [1] proved that provided 3 con-2 of 18 ditions are met: any networked system of arbitrarily large size, topological complexity, and balancing function form is stable.…”

Section: Review On the Stability Of Complex Networked Systemsmentioning

confidence: 99%

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Analysing region of attraction of load balancing on complex network

Zou

Guo

2022

Journal of Complex Networks

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Many complex engineering systems network together functional elements to balance demand spikes but suffer from stability issues due to cascades. The research challenge is to prove the stability conditions for any arbitrarily large and dynamic network topology with any complex balancing function. Most current analyses linearize the system around fixed equilibrium solutions. This approach is insufficient for dynamic networks with multiple equilibria, for example, with different initial conditions or perturbations. Region of attraction (ROA) estimation is needed in order to ensure that the desirable equilibria are reached. This is challenging because a networked system of non-linear dynamics requires compression to obtain a tractable ROA analysis. Here, we employ master stability-inspired method to reveal that the extreme eigenvalues of the Laplacian are explicitly linked to the ROA. This novel relationship between the ROA and the largest eigenvalue in turn provides a pathway to augmenting the network structure to improve stability. We demonstrate using a case study on how the network with multiple equilibria can be optimized to ensure stability.

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Section: Numerical Simulation and Resultsmentioning

confidence: 99%

Section: Review On the Stability Of Complex Networked Systemsmentioning

confidence: 99%

Analysing region of attraction of load balancing on complex network

Zou

Guo

2022

Journal of Complex Networks

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“…1) Review on Near Equilibrium Methods: Recent breakthroughs have developed the framework to analysis the relationship between microscopic (like local component dynamics), macroscopic (global dynamics) behaviors and network topology [4]- [7]. Our previous work in [1] proved that provided 3 conditions are met: any network of arbitrarily large size, topological complexity, and balancing function form is stable.…”

Section: A Review On the Stability Of Complex Network Systemsmentioning

confidence: 99%

Regions of Attraction Estimation using Level SetMethod for Complex Network System

Zou¹,

Huang²,

Guo³

2021

Preprint

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Many complex engineering systems network together functional elements and balance demand loads (e.g. information on data networks, electric power on grids). This allows load spikes to be shifted and avoid a local overload. In mobile wireless networks, base stations (BSs) receive data demand and shift high loads to neighbouring BSs to avoid outage. The stability of cascade load balancing is important because unstable networks can cause high inefficiency. The research challenge is to prove the stability conditions for any arbitrarily large, complex, and dynamic network topology, and for any balancing dynamic function.Our previous work has proven the conditions for stability for stationary networks near equilibrium for any load balancing dynamic and topology. Most current analyses in dynamic complex networks linearize the system around the fixed equilibrium solutions. This approach is insufficient for dynamic networks with changing equilibrium and estimating the Region of Attraction (ROA) is needed. The novelty of this paper is that we compress this high-dimensional system and use Level Set Methods (LSM) to estimate the ROA. Our results show how we can control the ROA via network topology (local degree control) as a way to configure the mobility of transceivers to ensure preservation of stable load balancing.

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Uncertainty Quantification of Multi-Scale Resilience in Nonlinear Complex Networks using Arbitrary Polynomial Chaos

Cited by 2 publications

References 26 publications

Analysing region of attraction of load balancing on complex network

Analysing region of attraction of load balancing on complex network

Regions of Attraction Estimation using Level SetMethod for Complex Network System

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