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Stochastic transitions in the Schlögl reaction model with nonextensive statistical noise and Gaussian white noise

In this paper, we investigate the stochastic transitions in a bistable Schlögl chemical reaction subjected to a nonextensive statistical noise (NESN) and a Gaussian white noise. The NESN is a correlated noise, and able to describe heavy-tailed noise distributions with certain deviation degree relative to Gaussian colored noise. With a unified-colored noise approximation method, the theoretical results of the steady state probability density function (PDF) and mean first passage time (MFPT) are obtained to demonstrate the influences of NESN. The validity of theoretical results has been confirmed by numerical simulations of the PDFs. Besides, stochastic P-bifurcation is discovered based on the changing of PDFs. The results show that the NESN will keep the conversion rate of substrate and the generation rate of products in the low state. Finally, from the MFPT, we find that the intensity and deviation degree of NESN, and Gaussian noise intensity can decrease the switching time between two states.