Asymmetric Lévy noise changed stability in a gene transcriptional regulatory system

Abstract

• Stability analysis of gene transcriptional regulatory system under asymmetric Lévy noise is meaningful but seldom reported before, and this article's study is about it. • A recently proposed stochastic basin of attraction (SBA) is used to explore the stability of the system. The SBA is built by escape probability. The comparison of Monte Carlo simulation (MCS) shows that the numerical scheme for solving escape probability is accurate enough to observe the influence of parameters on stability. • A new concept that is constructed using the stochastic basin of attraction and the stationary probability density function was used to determine the stable steady state of the system. The change of stability degree can be observed clearly by it. Perturbation of internal molecules in gene regulation is discontinuous and asymmetrical. Therefore, it is reasonable to use asymmetric Lévy noise to simulate environmental disturbance. However, there is limited research on the stability of systems under asymmetric Lévy noise. This study, based on the stochastic basin of attraction and mean first exit time, examines the stability of the gene transcriptional regulatory system. It is found that, by changing the skewness parameter of noise, the stability of the system can change significantly. Stochastic basin stability, a new concept based on the stochastic basin of attraction and the stationary probability density function, is then used to quantify the stability of the two states of the system. We demonstrate that merely modulating the dissipation coefficient does not change the effect of the skewness parameter on the stochastic basin of attraction.