Genetic transcriptional regulatory model driven by the time-correlated noises

Abstract

] are investigated in presence of two time-correlated noises. The steady state probability distribution can be obtained by solving the Fokker-Planck equation. It is found that both the correlated-time between the white noise and the colored noise and that between the colored noises can convert the bistability to monostability while the former activates the transcription and the latter suppresses it.

Steady state analysis for the effect of tumor microenvironmental factors on tumor growth dynamics driven by correlated noises

“…In application, the theoretical model equation is the Langevin stochastic equation and the corresponding Fokker Planck equation for the time evolution of probability density, and such theoretical descriptions have been used in different context to study the behavior of noise driven systems [1][2][3], where the driven noises are either Gaussian white or colored noises and in the form of additive or multiplicative. Research in [4] first discovered that physical systems driven by simultaneous noises with common origin leads to correlated effects, and the study of complex systems driven by correlated noises have been given much attention especially in bistable system [5][6][7], in mode laser system [8,9], in gene selection and genetic transcription regulatory models [10][11][12] and in all these systems, interesting properties and system behaviors were discovered at the influence of noise correlated effects. In the study of tumor cell growth, mathematical model equations that closely captures the general features of tumor growth are considered in literature, and logistic equation is the most widely used deterministic model for theoretical study [13].…”