Chernyshevsky Saratov State University , Russia

The dynamics of two coupled discrete maps is considered. The type of coupling is chosen in order not to introduce any additional dissipation in the system, so the dissipation level is determined only by the subsystem parameters. The decrease of dissipation leads to the complication of the parameter space structure and the picture of critical behaviour. Particularly, the line of transition to chaos via the Feigenbaum period- doubling cascade becomes divided into several fragments, the structure of the parameter space between them is rather interesting. Different mechanisms of this process are described.