Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices

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Abstract

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on the vector of real physical parameters p. We study perturbations of semi-simple multiple eigenvalues as well as perturbations of non-derogatory eigenvalues under small variations of p. Explicit formulae describing the bifurcation of the eigenvalues are derived. Application to the problem of excitation of unstable modes in rotating continua such as spherically symmetric MHD α2-dynamo and circular string demonstrates the efficiency and applicability of the approach.

Mathematics Subject Classification (2000)

Primary 34B08 Secondary 34D10 

Keywords

Operator matrix Non-self-adjoint boundary eigenvalue problem Keldysh chain Multiple eigenvalue Diabolical point Exceptional point Perturbation Bifurcation Stability Veering Spectral mesh Rotating continua 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Dynamics and Vibrations Group, Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

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