Asymmetric Lévy noise changed stability in a gene transcriptional regulatory system

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.