Most probable dynamics of a genetic regulatory network under stable Levy noise

Numerous studies have demonstrated the important role of noise in the dynamical behaviour of a complex system. The most probable trajectories of nonlinear systems under the influence of Gaussian noise have recently been studied already. However, there has been only a few works that examine how most probable trajectories in the two-dimensional system (MeKS network) are influenced under non-Gaussian stable Levy noise. Therefore, we discuss the most probable trajectories of a two-dimensional model depicting the competence behaviour in B. subtilis under the influence of stable Levy noise. On the basis of the Fokker-Planck equation, we describe the noise-induced most probable trajectories of the MeKS network from the low ComK protein concentration (vegetative state) to the high ComK protein concentration (competence state) under stable Levy noise. We demonstrate choices of the non-Gaussianity index alpha and the noise intensity epsilon which generate the ComK protein escape from the low concentration to the high concentration. We also reveal the optimal combination of both parameters alpha and epsilon making the tipping time shortest. Moreover, we find that different initial concentrations around the low ComK protein concentration evolve to a metastable state, and provide the optimal alpha and epsilon such that the distance between the deterministic competence state and the metastable state is smallest. (C) 2018 Elsevier Inc. All rights reserved.