Metamorphoses of characteristic curves in circulatory systems

Explicit formulae are developed for typical metamorphoses of characteristic curves in circulatory systems which depend on a vector of parameters. The formulae obtained utilize information on the system only at the point of confluence of the curves and enable one to analyse both qualitatively and quantitatively the behaviour of the oscillation frequencies in the neighbourhood of that point. Quadratic approximations are found for the domains of flutter and divergence, and the relation between the convexity properties of these domains and the type of metamorphosis of the characteristic curves is established.