Slow-fast oscillatory dynamics and phantom attractors in stochastic modeling of biochemical reactions

A problem of the probabilistic analysis of stochastic phenomena in slow-fast dynamical systems modeling biochemical reactions is considered. We study how multiplicative noise induces systematic shifts of probabilistic distributions and forms "phantom " attractors in nonlinear enzymatic models. The mathematical analysis of the underlying probabilistic mechanism of such stochastic transformations is performed by the "freeze-and-average " method. Our theoretical results are supported by direct numerical simulation. Published under an exclusive license by AIP Publishing.