Sign patterns that require or allow particular refined inertias

DOI10.1016/j.laa.2012.05.014zbMath1277.15023OpenAlexW2045472404MaRDI QIDQ448371

D. Dale Olesky, E. Bodine, Pauline van den Driessche, Louis Deaett, Judith Joanne Mcdonald

Publication date: 6 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.05.014

zbMATH Keywords

eigenvaluesHopf bifurcationdynamical systemsign patternrefined inertia

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Smooth dynamical systems: general theory (37C99) Sign pattern matrices (15B35)

Related Items (18)

Using sign patterns to detect the possibility of periodicity in biological systems ⋮ Characterization of star sign patterns that require \(\mathbb{H}_n\) ⋮ A mathematical model of syphilis transmission in an MSM population ⋮ A mathematical analysis of an activator-inhibitor Rho GTPase model ⋮ Refined inertias of strongly connected orientations of the Petersen graph ⋮ Unnamed Item ⋮ Sign Pattern Matrices ⋮ Path sign patterns of order \(n\geq 5\) do not require \(\mathbb{H}_n\) ⋮ Zero-nonzero tree patterns that allow Sn∗ ⋮ Sign patterns that require \(\mathbb{H}_n\) exist for each \(n\geq 4\) ⋮ A note on sign patterns of order 3 that require particular refined inertias ⋮ Sign patterns requiring a unique inertia ⋮ Stability of sign patterns from a system of second order ODEs ⋮ Sign pattern matrices that allow inertia \(\mathbb{S}_n\) ⋮ Zero-nonzero patterns of order \(n\geq 4\) do not require \(\mathbb{H}_n^\ast\) ⋮ Sets of refined inertias of zero-nonzero patterns ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• Refined inertias of tree sign patterns of orders 2 and 3
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Criterion of high-codimensional bifurcations with several pairs of purely imaginary eigenvalues
• Spectrally arbitrary patterns
• Refined inertially and spectrally arbitrary zero-nonzero patterns
• Generating potentially nilpotent full sign patterns
• Nonlinear Oscillations in Epidemic Models

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