Stochastic Genetic Regulatory Networks Research Articles

Passivity-based control and asymptotic synchronization for multi-variable discrete stochastic genetic regulatory networks with complex network dynamics

Passivity-based control and asymptotic synchronization for multi-variable discrete stochastic genetic regulatory networks with complex network dynamics

Weighted Pseudo-θ-Almost Periodic Sequence and Finite-Time Guaranteed Cost Control for Discrete-Space and Discrete-Time Stochastic Genetic Regulatory Networks with Time Delays

This paper considers the dual hybrid effects of discrete-time stochastic genetic regulatory networks and discrete-space stochastic genetic regulatory networks in difference formats of exponential Euler difference and second-order central finite difference. The existence of a unique-weight pseudo-θ-almost periodic sequence solution for discrete-time and discrete-space stochastic genetic regulatory networks on the basis of discrete constant variation formulation is discussed, as well as the theory of semi-flow and metric dynamical systems. Furthermore, a finite-time guaranteed cost controller is constructed to reach global exponential stability of these discrete networks via establishing a framework of drive, response, and error networks. The results indicate that spatial diffusions of non-negative dense coefficients have no influence on the global existence of the unique weighted pseudo-θ-almost periodic sequence solution of the networks. The present study is a basic work in the consideration of discrete spatial diffusion in stochastic genetic regulatory networks and serves as a foundation for further study.

Exponential convergence in the mean-square sense of nonlocal stochastic almost automorphic genetic regulatory lattice networks

This paper first establishes the lattice model for nonlocal stochastic genetic regulatory networks with reaction diffusions by employing a mix of the finite difference and Mittag–Leffler time Euler difference techniques. Second, the existence of a unique bounded almost automorphic sequence in distribution and global mean-square exponential convergence to the achieved difference model are investigated. An illustrative example is used to show the feasible of the works of the current paper.

Random periodic sequence of globally mean-square exponentially stable discrete-time stochastic genetic regulatory networks with discrete spatial diffusions

<abstract><p>This paper regards the dual effects of discrete-space and discrete-time in stochastic genetic regulatory networks via exponential Euler difference and central finite difference. Firstly, the global exponential stability of such discrete networks is investigated by using discrete constant variation formulation. In particular, the optimal exponential convergence rate is explored by solving a nonlinear optimization problem under nonlinear constraints, and an implementable computer algorithm for computing the optimal exponential convergence rate is given. Secondly, random periodic sequence for such discrete networks is investigated based on the theory of semi-flow and metric dynamical systems. The researching findings show that the spatial diffusions with nonnegative intensive coefficients have no influence on global mean square boundedness and stability, random periodicity of the networks. This paper is pioneering in considering discrete spatial diffusions, which provides a research basis for future research on genetic regulatory networks.</p></abstract>

Adaptive Finite-Time Control of Stochastic Genetic Regulatory Networks with Time-Varying Delays

This article discusses the finite-time stability problem for stochastic genetic regulatory networks (SGRNs) with time-varying delays. By designing suitable adaptive controllers and skillfully choosing appropriate Lyapunov and multi-Lyapunov functions, respectively, the above non-switched and switched SGRNs can achieve finite time stability in probability. Superior to some existing controllers for GRNs, the above adaptive design procedures can reduce the dependence of the system parameters. Finally, two numerical simulation examples illustrate the effectiveness of the theoretical results.

Robust Passivity Analysis of Stochastic Genetic Regulatory Networks with Levy Noise

Robust Passivity Analysis of Stochastic Genetic Regulatory Networks with Levy Noise

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

Improved stochastic integral inequalities to stability analysis of stochastic genetic regulatory networks with mixed time‐varying delays

This study investigates the problem of mean-square asymptotic stability analysis of stochastic genetic regulatory networks with mixed time-varying delays. The innovation of this study lies in that several stochastic integral inequalities are improved based on auxiliary function integral inequalities. Thereby, less conservative mean-square asymptotic stability criteria are derived by constructing Lyapunov–Krasovskii functional with multiple integral terms and employing the proposed stochastic integral inequalities and the (reciprocal) convex combination technique. The obtained stability criteria are described in terms of linear matrix inequalities, which can be easily verified by using standard software tools. Finally, three numerical examples are provided to test and verify the effectiveness and less conservativeness of the proposed stability criteria.

Event-Triggered Dissipative Filtering for Network-Based Stochastic Genetic Regulatory Networks Under Aperiodic Sampling

Based on event-triggered mechanism, networked dissipative filtering of stochastic genetic regulatory networks is investigated under aperiodic sampling. The states of the genetic regulatory network are sampled aperiodically and transmitted via a communication network to filters to estimate the expression levels of the mRNA and protein. In order to make better use of limited communication resources, a novel communication scheme is proposed. Then considering both network-induced delays and aperiodic sampling simultaneously, the filtering error dynamics are modeled in the form of a stochastic system with a time-varying delay. By Lyapunov theory and Wirtinger-based integral inequalities in a stochastic setting, asymptotical stability and dissipativity of the error dynamic system can be ensured. Based on the derived criterion, suitable dissipative filters are designed such that a set of inequalities are satisfied. Finally, the effectiveness of the proposed method is illustrated by a simulation example.

Global Dissipativity for Stochastic Genetic Regulatory Networks With Time-Delays

Genetic Regulatory Networks (GRNs) play an important role for the development and evolution of biological systems. On the basis of the development for DNA microarray technologies, a profound study for GRNs becomes possible at genome scale. In this article, the global dissipativity and corresponding attractive set for the GRNs with stochastic disturbances and time-delays are investigated based on Lyapunov theory. Stochastic disturbances are considered into both the feedback regulation process and the translation process for reflecting the inherent noise perturbations on a foundation of factual knowledge. Through the resort to the several appropriate Lyapunov-Krasovskii Functionals (LKFs) combining with Ito’s formula and different inequality techniques, some corresponding sufficient conditions and the attractive set are obtained for the GRNs in linear matrix inequality form, which are easy to verify by the numerical software. Finally, one three-node GRN is proposed and analyzed to illustrate the validity of the proposed results by using the Field-Programmable Gate Array (FPGA) hardware simulation tool.

Stabilization of Switched Stochastic Genetic Regulatory Networks with Leakage and Impulsive Effects

In this paper, the global asymptotical stability analysis problem is considered for stabilization of switched stochastic genetic regulatory networks with leakage and impulsive effects. Using the method of Lyapunov function, sufficient conditions are derived based on the linear matrix inequality (LMI) technique, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Finally, two numerical examples are given to expo the capability and efficiency of our results.

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov–Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

A state estimation H∞ issue for discrete-time stochastic impulsive genetic regulatory networks in the presence of leakage, multiple delays and Markovian jumping parameters

In this work, we probes the stability results of H∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. An example is presented to illustrate our results of the mean-square exponential stability analysis.

Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays

In this paper, the event-triggered H∞ state estimation problem is investigated for a class of discrete-time stochastic genetic regulatory networks with both Markovian jumping parameters and time-varying delays. The jumping parameters are governed by a homogeneous Markovian chain and the time-varying delays under consideration occur in both the feedback regulatory process and transcription process. The aim of this paper is to estimate the concentrations of mRNA and protein in such genetic regulatory networks by using the available measurement outputs. In order to reduce the information communication burden, the event-triggered mechanism is adopted and the measurement outputs are only transmitted to the estimator when a certain triggered condition is met. By constructing an appropriate Lyapunov functional, some sufficient conditions are derived under which the estimation error dynamics is stochastically stable and the H∞ performance constraint is satisfied. Based on the analysis results, the desired H∞ estimator parameters are designed in terms of the solution to a set of matrix inequalities that can be easily solved by the Matlab toolboxes. Finally, a simulation example is provided to illustrate the effectiveness of the proposed event-triggered state estimation scheme.

Finite-time stochastic synchronization of genetic regulatory networks

This paper is concerned with the finite-time synchronization for a class of stochastic genetic regulatory networks (GRNs). The purpose of the addressed problem is to design a controller that can synchronize the concentration of the mRNA and the protein of GRNs in finite time with probability. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are first established for ensuring the finite-time stochastic stability of synchronization error in probability. Then, the gain parameters of the controller are obtained by solving a linear matrix inequality and the robust finite-time synchronization is guaranteed for GRNs with uncertain parameters. Compared with the previous references, a continuous finite-time controller is designed to achieve the synchronization objective and a constructive method that may accelerate the convergence is discussed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

Delay-dependent robust [formula omitted] filtering of uncertain stochastic genetic regulatory networks with mixed time-varying delays

In this paper, the robust H∞ filtering problem for uncertain stochastic genetic regulatory networks (GRNs) with mixed time-varying delays is involved. The uncertain stochastic GRNs under consideration are extended to involve Itô-type stochastic disturbance, norm-bounded parameter uncertainties, and time-varying discrete and distributed delays. By constructing a proper Lyapunov–Krasovskii functional and using reciprocal convex technique, sufficient conditions in terms of linear matrix inequalities were presented to guarantee that the filtering error systems are mean-square robustly asymptotically stable with disturbance attenuation level γ. In the end, two numerical examples are given to illustrate the effectiveness of the proposed approach.

Stochastic Stability Analysis for Switched Genetic Regulatory Networks with Interval Time-Varying Delays Based on Average Dwell Time Approach

In this article, the problem of stochastic stability analysis for switched stochastic genetic regulatory networks with interval time-varying delays based on average dwell time approach is investigated. By constructing the piecewise Lyapunov-Krasovskii functional, delay-dependent stability conditions are derived by using free-weighting matrix and convex combination approach. The derived stability conditions are expressed in terms of linear matrix inequalities which can be easily solved by using the MATLAB LMI control toolbox. Finally, numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed theoretical results.

Stochastic stability of switched genetic regulatory networks with time-varying delays.

This paper investigates the exponential stability problem of switched stochastic genetic regulatory networks (GRNs) with time-varying delays. Two types of switched systems are studied respectively: one is the stochastic switched delayed GRNs with only stable subsystems and the other is the stochastic switched delayed GRNs with both stable and unstable subsystems. By using switching analysis techniques and the modified Halanay differential inequality, new criteria are developed for the exponential stability of switched stochastic GRNs with time-varying delays. Finally, an example is given to illustrate the main results.

Exponential Stability of Stochastic Genetic Regulatory Networks with Interval Uncertainties and Multiple Delays

In this paper, the delay-dependent exponential stability analysis problem for a class of genetic regulatory networks (GRNs) with multiple time-varying delays and interval parameter uncertainties is studied. By employing a new Lyapunov–Krasovskii functional and employing some free-weighting matrices, we derive sufficient delay-dependent conditions ensuring the exponential stability of interval GRNs with multiple time-varying delays and stochastic perturbations in the form of linear matrix inequalities. Finally, three numerical examples are used to demonstrate and verify the advantages of the main results.