ABOUT 2 MECHANISMS OF REUNION OF CHAOTIC ATTRACTORS

Considering a family of two-dimensional piecewise linear maps, we disc uss two different mechanisms of reunion of two (or more) pieces of cyc lic chaotic attractors into a one-piece attracting set, observed in se veral models. It is shown that, in the case of so-called 'contact bifu rcation of the 2(nd) kind', the reunion occurs immediately due to homo clinic bifurcation of some saddle cycle belonging to the basin boundar y of the attractor. In the case of so-called 'contact bifurcation of t he 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 bifur cation of a saddle cycle on the basin boundary. (C) 1998 Elsevier Scie nce Ltd. All rights reserved.