an asymptotically stable attractor of the 2-dimensional autonomous systems.

It is not easy to distinguish these two types of pull back attractors from simple observation. For the case of SNA, however, there should exist a repelling orbit (that should be a part of a repeller) in arbitrarily small neighborhood of the pull back attractor[@Sturman-Stark-00]. Thus we could expect that there exist trajectories of $\tilde M$ starting from a point in an arbitrarily small neighborhood of an “SNA” but finally attracted to another attractor (of $\tilde M$) that corresponds to the basin of repulsion of the repeller which is located in touch with the attractor(SNA). Thus, it is expected that SNAs exhibit a kind of sensitivity of final state against arbitrarily small perturbation in the neighborhood of the attractor in $\tilde M$, like those attractors with “riddled” basin[@Alexander-ETAL-92; @Yang-01]. We try to detect this presumed type of sensitivity of final state in $\tilde M$ expected for SNAs, by checking whether a small perturbation for $w$ component of $\tilde M$ would make the destination of the trajectory to another attractor (in $w>0$ region) or not. Thus we introduce a “perturbed” version of segment map $\tilde M^+$, given as $\tilde
M^+ = \tilde 