Mechanisms complicating the dependence of the transient process duration on the initial conditions in two-dimensional maps

Mechanisms leading to complication of the dependence of a transient process duration on the initial conditions upon a change in control parameters of a two-dimensional dynamical system with discrete time (Eno map) are considered. It is shown that the character of this dependence for a stable cycle is determined by multiplicators. A change in the control parameters in the same dynamical regime produces a bifurcation leading to reclosure of the stable and unstable manifolds. This results in a qualitative complication of the dependence of the transient process duration on the initial conditions in the system.