Stability of gene regulatory networks with Lévy noise

The stability of gene regulatory networks has attracted substantial research efforts in the field of systematic biology. Actual gene regulatory networks are always subject to noise interference and disruption to the organism either internally or externally. Specifically, the special case of instantaneous mutation may exist in gene regulatory networks at the mRNA or protein level. Compared with other existing models, a Levy noise-driven gene regulatory network model has been proved to be more realistic, since it is a powerful tool to describe the above special case. On the basis of previous studies, we developed a theoretical proof of the Levy noise- driven gene regulatory network, and carried out a large number of numerical simulations for validation. Based on adequate analysis of the simulation examples, the sufficient conditions were investigated and are presented herein to obtain the global asymptotic stability of gene regulatory networks with time-varying delays and Levy noise.