Dynamical behavior of the activator–repressor circuit model under random fluctuations

Lévy noise-induced transitions in gene regulatory networks

“…Nevertheless, we have managed to calculate these deterministic quantities by accurate and efficient numerical methods. 13,[31][32][33][34][35] The noise intensities σ k , σ s , ε k , ε s , the Lévy motion index α (relating with the jump magnitude and its frequency) have important and subtle influences on MFET and FEP. We have used the relative contribution factor (RCF) λ , the ratio between non-Gaussian and Gaussian noise strengths, to implement optimal control in the transition between the two states, when the total quantities of the noise intensities are fixed.…”

“…50 Then the generator A is Secondly, the AMFET on D is defined as ū(D) = 1 |D| D u(k, s)dkds for our analysis from the macroscopic perspective. 6,35 First escape probability (FEP) and average first escape probability (AFEP). The escape probability here are employed to characterize the likelihood of the transition between the low vegetative and the high competence region for the MeKS system.…”

“…The AFEP on D is defined as p(D) = 1 |D| D p(k, s)dkds. 6,35 We use the FEP to examine the transitions from a microscopic viewpoint, and the AFEP from the macroscopic perspective.…”

“…Nevertheless, we have managed to apply recent results to calculate these deterministic quantities by accurate and efficient numerical methods. 13,[31][32][33][34][35] Numerical methods. To solve the MFET and the FEP efficiently and accurately, Gao et al 31 constructed an effective numerical method to solve the aforementioned differential-integral equations.…”

“…However, it becomes more challenging but difficult to conduct such a simulation in the two-dimensional model with Lévy motions. Nevertheless, we manage to calculate these deterministic quantities by accurate and efficient numerical methods, 13,[31][32][33][34][35] instead of Monte-Carlo simulation.…”