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.

Automated summary

This paper considers the problem of probabilistic analysis of stochastic phenomena in slow-fast dynamical systems modeling biochemical reactions. It studies 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 using the freeze-and-average method. The theoretical results are supported by direct numerical simulation.