Slow-fast oscillatory dynamics and phantom attractors in stochastic modeling of biochemical reactions
Irina Bashkirtseva1, Lev Ryashko1
1Department of Theoretical and Mathematical Physics, Ural Federal University, Lenina, 51, 620000 Ekaterinburg, Russia.
Abstract:
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.
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