Asymptotic stability of Markovian switching genetic regulatory networks with leakage and mode-dependent time delays

Abstract

The problem of stability analysis of Markovian switching genetic regulatory networks (GRNs) with leakage and mode-dependent time-varying delays along Brownian motions is reported here. The GRNs are composed of N modes which switches from one mode to another according to a Markov chain with known transition probabilities. The regulatory functions of GRNs are assumed to be sector-like nonlinear functions. By applying delay-fractioning approach, the sufficient conditions are derived to guarantee the stability of Markovian switching GRNs with leakage and mode-dependent time-varying delays in the mean-square sense. Also, the corresponding results are obtained for the GRNs without leakage delays. To illustrate the effectiveness of the proposed theoretical results, repressilator model of Escherichia coli is analyzed in the end.