A Stochastic Gene Expression Regulation Model with Markov Switching
Both white noise and Markov switching are introduced to study the dynamics of gene cooperative expression system.The random attraction set of the model is constructed based on the random comparison principle.The conclusion shows that the solution of the system is uniformly bounded under the influence of environmental noise.It is proved that the model has a unique ergodic sta-tionary distribution and the solution of the system is ergodic by constructing a suitable Lyapunov function.Some numerical simula-tions are carried out to support the results,and the numerical results show that the bistable phenomenon exists in the model studied,which is of great significance for the research of cell differentiation and other biological fields.
Brownian motionorder-preserving systemMarkov chainrandom attracting setstationary distribution