Parameter identification of genetic regulatory network with time-varying delays via adaptive synchronization method

Abstract

In this paper, the parameter identification of gene regulatory network with time-varying delay is studied. Firstly, we introduce the differential equation model of gene regulatory network with unknown parameters and time delay. Secondly, for the unknown parameters in the time-varying model, a corresponding system with adaptive parameters and adaptive controller is introduced, and the parameter identification problem of the original model is transformed into the synchronization problem of the two systems. Thirdly, we design an effective adaptive controller and an adaptive law for parameters and construct a Lyapunov functional. Then we give a strict theoretical proof that the adaptive parameters can converge to unknown parameters by Barbalat's lemma. Finally, a numerical example is given to verify the validity of the theoretical results.

Adaptive Generalized Synchronization between Circuit and Computer Implementations of the Rössler System

“…The most prominent example is parameter identification, because adjusted parameters of the slave system can then often be directly measured and related to uncertain parameters of the master system [10,[13][14][15]. Particular examples in which this approach has been used are the design of a secure communication system [9], parameter identification of a gene regulatory network [16] and investigation of circadian rhythms in mammals [17]. It also may be used in chaotic sensors, typically consisting of a master system which serves as a measurement unit and a slave system which serves as a reference [18,19].…”