On the Spatial Pattern of Input-Output Metrics for a Network Synchronization Process

Subir Sarker; Sandip Roy

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arXiv · 2207.10868

On the Spatial Pattern of Input-Output Metrics for a Network Synchronization Process

Subir Sarker·Sandip Roy

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Abstract

A graph-theoretic analysis is undertaken for a compendium of input-output (transfer) metrics of a standard discrete-time linear synchronization model, including lp gains, frequency responses, frequency-band energy, and Markov parameters. We show that these transfer metrics exhibit a spatial degradation, such that they are monotonically nonincreasing along vertex cutsets away from an exogenous input. We use this spatial analysis to characterize signal-to-noise ratios (SNRs) in diffusive networks driven by process noise, and to develop a notion of propagation stability for dynamical networks. Finally, the formal results are illustrated through an example.

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Subir Sarker, Sandip Roy. 2022-07-22. On the Spatial Pattern of Input-Output Metrics for a Network Synchronization Process. https://arxiv.org/abs/2207.10868

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