Nonlocal Dynamics for Non-Gaussian Systems Arising in Biophysical Modeling

The aim of this article is to review our recent work on nonlocal dynamics of non-Gaussian systems arising in a gene regulatory network. We have used the mean exit time, escape probability and maximal likely trajectory to quantify dynamical behaviors of a stochastic differential system with non-Gaussian $$\alpha$$-stable Levy motions, to examine how the non-Gaussianity index and noise intensity affect the gene transcription processes.