DOUBLE CRISES IN 2-PARAMETER DYNAMICAL-SYSTEMS

A crisis is a sudden discontinuous change in a chaotic attractor as a system parameter is varied. We investigate phenomena observed when two parameters of a dissipative system are varied simultaneously, followi ng a crisis along a curve in the parameter plane. Two such curves inte rsect at a point we call a double crisis vertex. The phenomena we stud y include the double crisis vertex at which an interior and a boundary crisis coincide, and related forms of double crisis. We show how an e xperimenter can infer a crisis from observations of other related cris es at a vertex.