Variation of the dependence of the transient process duration on the initial conditions in systems with discrete time

Dependence of the transient process duration on the initial conditions is considered in one-and two-dimensional systems with discrete time, representing a logistic map and the Eno map, respectively. It is shown that dependence of the transient process duration on the initial conditions for a cycle of period 1 is determined by multiplicators of a stable immobile point. A change in the control parameters within the same dynamical regime results in bifurcation leading to a qualitative change in the above dependence.