Noise-induced bifurcations in the stochastic chemostat model with general nutrient uptake functions

Noise distorts the epigenetic landscape and shapes cell-fate decisions

“…In stochastic dynamics there is potential for richer dynamics (see e.g. [110] and [111]), and we commonly distinguish between two types of bifurcations [112]: D-bifurcations, are the analogues of deterministic bifurcations; the 'D' stands for 'dynamical' and this type of bifurcation reflects sudden changes in the sign of the leading Lyapunov exponent of the dynamics [113]. P-bifurcations, by contrast, reflect sudden changes in the steady-state probability distribution over states.…”

Stationary probability density of a stochastic chemostat model with Monod growth response function

“…It should be noticed that the SPDs in the above works can be obtained by solving the corresponding Fokker Planck-Kolmogorov (FPK) equations which can be easily achieved. Different from the scalar stochastic models considered in the literature, 22,24 some researches derived the SPDs for two-dimensional stochastic differential equations by using the polar coordinate transformation and stochastic averaging method. [25][26][27][28][29] For instance, Huang et al 25 presented a stochastic dynamical model on a typical HAB algae diatoms and dinoflagellates and analyzed its stochastic bifurcation based on the corresponding SPD.…”

“…The theoretical and numerical results show that the shape of SPD will experience a transition from one structure to another as the feasible parameter passes through a critical value, that is, the stochastic model may exist phenomenological bifurcation 23 . Zhao and Yuan 24 found the phenomenological bifurcation point for a stochastic single‐species chemostat model which can be reduced to a one‐dimensional stochastic system. It should be noticed that the SPDs in the above works can be obtained by solving the corresponding Fokker Planck‐Kolmogorov (FPK) equations which can be easily achieved.…”