A dynamical system can be represented by
x ex fuY y gxY
where A is a square matrix and B, C are rectangular matrices.
The question of uncertain parameters e in the entries of the matrices A, B, C is particularly important when using the Kronecker form of the triple of matrices eY fY g: the eigenstructure may depend discontinuously on the parameters when the matrices eeY feY ge depend smoothly on those parameters.
It is of great interest to know which dierent structures can arise from small perturbations of a dynamical system, and discuss the generic behaviour of smooth fewparameter families of linear systems. A fundamental way of dealing with these problems is, in a ®rst step, to stratify the space of triples of matrices de®ning the systems. Here an important role is played by the miniversal deformations.
A second step is to induce a partition in the space of parameters parametrizing the family of linear systems. We need to consider transversal families in order to ensure that the induced partition (called the bifurcation diagram) is also a strati®cation. In this case the induced partition is called a bifurcation diagram.