  The principal aim of this work is the evidence on empirical way that
catastrophic bifurcation breakdowns or transitions, proceeded by flickering
phenomenon, are present on notoriously significant and unpredictable financial
markets. Overall, in this work we developed various metrics associated with
catastrophic bifurcation transitions, in particular, the catastrophic slowing
down (analogous to the critical slowing down). All these things were considered
on a well-defined example of financial markets of small and middle to large
capitalization. The catastrophic bifurcation transition seems to be connected
with the question of whether the early-warning signals are present in financial
markets. This question continues to fascinate both the research community and
the general public. Interestingly, such early-warning signals have recently
been identified and explained to be a consequence of a catastrophic bifurcation
transition phenomenon observed in multiple physical systems, e.g. in
ecosystems, climate dynamics and in medicine (epileptic seizure and asthma
attack). In the present work we provide an analogical, positive identification
of such phenomenon by examining its several different indicators in the context
of a well-defined daily bubble; this bubble was induced by the recent worldwide
financial crisis on typical financial markets of small and middle to large
capitalization.
