On matrices with common invariant cones with applications in neural and gene networks

DOI10.1016/j.laa.2004.04.005zbMath1070.15017OpenAlexW2161993753WikidataQ57942489 ScholiaQ57942489MaRDI QIDQ1774987

Roderick Edwards, Michael J. Tsatsomeros, Judith Joanne Mcdonald

Publication date: 4 May 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2004.04.005

zbMATH Keywords

neural networkinvariant subspacenonnegative matrixCantor settensor productPerron-Frobeniusproper conegene networkexterior productcompound matrixinvariant conedominant eigenvectordecomposable vectorGlass networkmatrix word

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Positive matrices and their generalizations; cones of matrices (15B48) Exterior algebra, Grassmann algebras (15A75)

Related Items (9)

Geometric properties of a class of piecewise affine biological network models ⋮ On common invariant cones for families of matrices ⋮ Polytope Lyapunov functions for stable and for stabilizable LSS ⋮ Unnamed Item ⋮ Common non-trivial invariant closed cones for commuting contractions ⋮ Invariant multicones for families of matrices ⋮ When do several linear operators share an invariant cone? ⋮ A constructive approach to robust chaos using invariant manifolds and expanding cones ⋮ Periodic solutions of gene networks with steep sigmoidal regulatory functions

Cites Work

• Common eigenvectors of two matrices
• A criterion for the existence of common invariant subspaces of matrices
• Chaos in high-dimensional neural and gene networks
• Chaos in neural and gene networks with hard switching
• Analysis of continuous-time switching networks
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