Topological Detection of Phenomenological Bifurcations with Unreliable Kernel Densities

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations requires reliable kernel density estimates computed from an ensemble of system realizations. However, in several real world signals such as Big Data, only a single system realization is available -- making it impossible to estimate a reliable kernel density. This study presents an approach for detecting P-type bifurcations using unreliable …

art big current detection ensemble function kernel math.at math.ds pdf probability state state of the art stat.me stat.ml stochastic systems topology type world