Are the flows of complex-valued Laplacians and their pseudoinverses related?

dc.contributor.authorSaxena, Aditi
dc.contributor.authorTripathy, Twinkle
dc.contributor.authorAnguluri, Rajasekhar
dc.date.accessioned2024-12-11T17:01:57Z
dc.date.available2024-12-11T17:01:57Z
dc.date.issued2024-11-14
dc.description.abstractLaplacian flows model the rate of change of each node's state as being proportional to the difference between its value and that of its neighbors. Typically, these flows capture diffusion or synchronization dynamics and are well-studied. Expanding on these classical flows, we introduce a pseudoinverse Laplacian flow system, substituting the Laplacian with its pseudoinverse within complex-valued networks. Interestingly, for undirected graphs and unsigned weight-balanced digraphs, Laplacian and the pseudoinverse Laplacian flows exhibit an interdependence in terms of consensus. To show this relation, we first present the conditions for achieving consensus in the pseudoinverse Laplacian flow system using the property of real eventually exponentially positivity. Thereafter, we show that the pseudoinverse Laplacian flow system converges to consensus if and only if the Laplacian flow system achieves consensus in the above-mentioned networks. However, these are only the sufficient conditions for digraphs. Further, we illustrate the efficacy of the proposed approach through examples, focusing primarily on power networks.
dc.description.urihttp://arxiv.org/abs/2411.09254
dc.format.extent6 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifierdoi:10.13016/m2ojvo-qlhf
dc.identifier.urihttps://doi.org/10.48550/arXiv.2411.09254
dc.identifier.urihttp://hdl.handle.net/11603/37010
dc.language.isoen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Computer Science and Electrical Engineering Department
dc.rightsAttribution 4.0 International CC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectElectrical Engineering and Systems Science - Systems and Control
dc.subjectComputer Science - Systems and Control
dc.titleAre the flows of complex-valued Laplacians and their pseudoinverses related?
dc.typeText
dcterms.creatorhttps://orcid.org/0000-0003-2537-2778

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