Switch dynamics in a genetic toggle network driven by Lévy noise

The noise may drive the genetic toggle network switch from one stable state to another. To describe transcriptional bursting in synthesis process of biochemical systems, the Lévy noise is introduced to genetic toggle network with kinetic parameters and the dynamical transition is investigated via two deterministic quantities, the first escape probability and mean first exit time. Firstly, the analytical expressions of that two deterministic quantities in irregular domain are derived from the governing differential-integral equation. Then, the numerical schemes of the two indexes are developed by the finite difference method, and the validity of the proposed method is verified by the Monte Carlo simulations. Analyzing the Lévy noise on the switch mechine, we found that a decreasing stability index or an increasing noise intensity can reduce the probability of the first switching from the (low, high) state to the (high, low) state. Furthermore, higher noise intensity and stability index shorten the residence time of the (low, high) state.