About two mechanisms of reunion of chaotic attractors

Considering a family of two-dimensional piecewise linear maps, we discuss two different mechanisms of reunion of two (or more) pieces of cyclic chaotic attractors into a one-piece attracting set, observed in several models. It is shown that, in the case of so-called 'contact bifurcation of the 2(nd) kind', the reunion occurs immediately due to homoclinic bifurcation of some saddle cycle belonging to the basin boundary of the attractor. In the case of so-called 'contact bifurcation of the 1(st) kind', the reunion is a result of a contact of the attractor with its basin boundary which is fractal, including the stable set of a chaotic invariant hyperbolic set appeared after the homoclinic bifurcation of a saddle cycle on the basin boundary. (C) 1998 Elsevier Science Ltd. All rights reserved.