Almost sure stability of stochastic gene regulatory networks with mode-dependent interval delays.

Altwasser R, Guthke R, Vlaic S, Emmett MR, Conrad CA, Meyer-Baese A (2013) Almost sure stability of stochastic gene regulatory networks with mode-dependent interval delays. In: Proc. BIOCOMP'13, BIOCOMP'12, Proc. 13th Int. Conf. Bioinformatics and Computational Biology, Las Vegas/USA, 09/16/2012-09/19/2012, pp. 468-477.CSREA Press, Las Vegas, USA. ISBN: 1-60132-234-8.

Abstract

We investigate the almost surely asymptotic stability of gene regulatory networks
(GRNs) with Markovian switching. Previous research has described GRNs as cou-
pled nonlinear stochastic systems under parametric perturbations without consid-
ering the important aspect of different time-delays in the subsystems. However,
a realistic model of a GRN is that of a hybrid stochastic retarded system that
represents a complex nonlinear dynamical system including mode-dependent time
delays and Markovian jumping as well as noise fluctuations. In this paper, we in-
terpret GRNs as hybrid stochastic retarded systems and prove their almost surely
asymptotical stability and give upper bounds of derivatives of time delays of the
subsystems. The theoretical results are elucidated in an illustrative example and
thus shown how they can be applied to reverse engineering design.

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