Critical point of accumulation of fold-flip bifurcation points and critical quasi-attractor (the review and new results)

In paper we suggest an example of system which dynamics is answered to conception of a «critical quasi-attractor». Besides the brief review of earlier obtained results the new results are presented, namely the illustrations of scaling for basins of attraction of elements of critical quasi-attractor, the renormalization group approach in the presence of additive uncorrelated noise, the calculation of universal constant responsible for the scaling regularities of the noise effect, the illustrations of transitions initialized by noise that are realized between coexisted attractors.