The Stability Of Complex System With Leakage Time-delay

In this paper, the stability of the neural networks and gene regulatory networks aredeeply discussed. Artificial neural network is proposed because it has the human nervousfunction. This is widely used for artificial intelligence, signal processing, image processing,pattern recognition, nonlinear dynamics and logistics system. Time delay is inevitable for thelimited signal transmission speed, and it even may affect the stability of the system. Forexample, shock, cycle and diver gent. So the stability of time delay neural network has beenwidespread concern of scholars in both domestic and overseas. In addition, due to thedevelopment of science and technology, the completion of the genome sequencing, theemergence of high-performance computers and the determination of a large-scale geneexpression level of gene chip technology make it possible to study on the gene expression byuse of simulation methods. Due to the development, stability of gene network will help us toexplore its internal evolution mechanism, and the change trend can help us better understandthe gene regulatory network, so we can predict the trend of gene networks, so as to guide theclinical practice and to reveal the mystery of life. So, the study on the stability of geneticregulatory networks has become one of the hot topics of research in both domestic andoverseas.In this dissertation, based on the matrix theory, Lyapunov-Krasovskii functional method,inequality techniques and the Lyapunov stability theory for stochastic differential equation, anthoroughly investigation on the stability of gene regulatory network and neural networkmodels is built.The paper mainly studies that the stability problem of networks with time delays, first itstudies the stability of uncertain impulsive stochastic genetic regulatory networks withtime-varying delay in the leakage term, the second the stability of uncertain impulsivestochastic fuzzy neural networks with two additive time delays in the leakage term, the lastthe stability of stochastic neural networks with time-varying delay leakage term. At the end ofthe paper, it discusses how to study parameters of random with forgotten time delay disturbspulse gene networks mean square stability of the equilibrium point.Include the following content concretely:1. We study the stability of stochastic neural networks with time-varying delay leakageterm. The Lyapunov-Krasovskii stability theory is applied and combined with liner matrixinequality and important inequalities and the free-weighting matrices. Then we can getconditions which can guarantee the stability of the considered model.2. We study the stability of uncertain impulsive stochastic fuzzy neural networks withtwo additive time delays in the leakage term. By utilizing new Lyapunov-Krasovskii functionsand combined with liner matrix inequality and important inequalities and the free-weightingmatrices. The stability criterion is proposed in terms of linear matrix inequality (LMI).3. We study the stability of uncertain impulsive stochastic genetic regulatory networkswith time-varying delay in the leakage term. The Lyapunov-Krasovskii stability theory isapplied and combined with liner matrix inequality and important inequalities and thefree-weighting matrices. Then a criterion is derived to guarantee the stability of theconsidered neural networks. In addition, we also consider the stability of the model whichdoes not contain random items.For all the above studies, we use Matlab to program and obtain simulation results. Thesimulation results are in agreement with the conclusions. In addition, the inference in thearticle gives the judgment that whether genes complex systems without random term in theof the equilibrium is stable conditions or not.To illustrate the validity of research results, numerically solving LMI of the MATLABtoolbox and runge kutta algorithm for numerical simulation is used to the conditions oftheorem. And the simulation results showed the effectiveness of the method.