  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 and on the vector of real
physical parameters. We study perturbations of semi-simple multiple eigenvalues
as well as perturbations of non-derogatory eigenvalues under small variations
of the parameters. 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 alpha2-dynamo and
circular string demonstrates the efficiency and applicability of the theory.
