Isospectral graph transformations, spectral equivalence, and global stability of dynamical networks

DOI10.1088/0951-7715/25/1/211zbMath1247.05226arXiv1010.3272OpenAlexW2962867160MaRDI QIDQ3114636

Leonid A. Bunimovich, Benjamin Z. Webb

Publication date: 19 February 2012

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3272

zbMATH Keywords

dynamical networksgraph reductionisospectral graph transformationsnetwork's adjacency matrix

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Applications of graph theory to circuits and networks (94C15) Stability theory for smooth dynamical systems (37C75) Signed and weighted graphs (05C22)

Related Items (12)

A simple stability criterion for dynamical systems with stochastic switching and/or stochastic time-delays ⋮ Equitable decompositions of graphs with symmetries ⋮ Extensions and applications of equitable decompositions for graphs with symmetries ⋮ Isospectral reduction in infinite graphs ⋮ Isospectral compression and other useful isospectral transformations of dynamical networks ⋮ Pseudospectra of isospectrally reduced matrices ⋮ Stationary measures on infinite graphs ⋮ Isospectral reductions and quantum walks on graphs ⋮ Spectral and Dynamic Consequences of Network Specialization ⋮ Isospectral graph reductions and improved estimates of matrices' spectra ⋮ Characterizing cospectral vertices via isospectral reduction ⋮ Eigenvectors of isospectral graph transformations

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