Based On The Dynamic Model Of The Neural Network Stability

Since 1982 American California Engineering institute physicist J.Hopfield proposed Hopfield neural networks models, Artificial neural networks theory and applied research has been attracted more and more attentions. Artificial neural networks can carries on the different information processing, such as artificial intelligence, secure communications, network optimization, military information, pattern recognition, etc. Using the domain is widespread, including biology, computer science, management science, sociology as well as economic. Neural network was successfully applied in these areas are greatly dependent on system's dynamic characteristic. The stability is one of neural network very important dynamic characteristics. The stability is a key feature in designing a practical application system. Known to us, neural networks is unstable system in theory which is impossible to be carried in practical application. Under such premise and the background, the research neural network's stability has the theory and the practical significance.From the late 20 th century to the early 21 st century, More than a decade's time, life science, especially molecular biology science, had great surprising changes. On the one hand, due to the rapid development of genome sequencing and proteomics, a large amount of experimental data has been accumulated in biology. How to dig out basic laws of biological science by a large number of experimental data became the focus probles in life sciences. On the other hand, the research of information processing in biological systems has transformed from qualitative description of the single signal transduction pathway to quantitative description of complex protein and gene regulatory network. These advances make people believe that the 21st century is the century of life sciences. And biologists have gradually recognized that the reacher of life sciences need quantitative disciplines involved such as mathematics, physics, chemistry, information science and so on. With the development of bioinformatics, a growing number of mathematical methods applied to experimental data mining. There are a number of intelligent algorithms and statistical methods. Using these methods in genetic information accelerate our work. In this paper we propose a new method to build gene regulatory networks. This method finds out the relationship between genes by the time series experimental data. In the era of life sciences we presents a new method to build gene regulatory networks that is of practical significance.This paper is divided into two major parts. The first part is to study stability of dynamic neural networks models. The stability theories and methods are used to the research on the neural network stability. In this paper, we mainly research stability of impulsive neural networks with unbounded time-varying delays and continuously distributed delays, stability of stochastic impulsive neural networks with unbounded time-varying delays, stability of uncertain stochastic impulsive neural networks with unbounded time-varying delays and continuously distributed delays, and stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. We will can apply these theoretical results to build practical models,and design neural networks systems of the better satisfied actual situation. In the second part, gene regulatory networks are built by by the time series experimental data. We used mainly Ramsay's algorithm and Gauss-Newton algorithm.The main contents and originalities in this paper can be summarized as follows:1. For the impulsive neural networks model with unbounded time-varying delays and continuously distributed delays(?)By constructing reasonable Lyapunov-Krasovski functional, we give some LMI conditions forμ-stability of neural networks. Some sufficient conditions are estabilished for global boundedness and exponential stability of the equilibrium point. A special pulses, J k ( x(tk?))=?diag ( d1( k ),d2(k),..., d n(k)), is discussed. When d i( k)∈[0,2],i=1,2,...,n, pulses do not influence the stability of neural networks. Last, a numerical example is provided to demonstrate the effectiveness of the obtained results by resorting to LMI software package of MATLAB, and the graphical representation is used to explain our results.2. For stochastic impulsive neural networks model with unbounded time-varying delays (?)By constructing reasonable Lyapunov-Krasovski functional, using the random analysis theory and impulsive control method, we give some LMI conditions forμ-stability in the mean sense . When the diffusion coefficientσ(t ,g(y(t)),g(y(t?τ(t)))≡0, aμ-stable criteria for neural networks with unbounded time-varying delays is given. A global boundedness is given on neural networks system. Last, two numerical examples are provided to demonstrate the effectiveness of the obtained results by resorting to LMI software package of MATLAB.3. For parameter uncertain stochastic impulsive neural networks model with unbounded time-varying delays and continuously distributed delays (?)First, we investigate the global stability in the mean sense of stochastic impulsive neural networks with unbounded time-varying delays and continuously distributed delays. By means of Lyapunov-Krasovski functional , the linear matrix inequality (LMI) approach, the random analysis theory and impulsive control method, stability criteria in the stochastic mean are presented. When the diffusion coefficientσ(t ,g(y(t)),g(y(t?τ(t)))≡0, aμ-stable criteria for neural networks with unbounded time-varying delays and continuously distributed delays is derived. Then, we investigate the global robust stability in the mean sense of parameter uncertain stochastic impulsive neural networks with unbounded time-varying delays and continuously distributed delays. Parameter uncertainties are time-varying and norm-bounded. Based on Lyapunov-Krasovskii functional and stochastic analysis approaches, some new robustμ-stability criteria in the mean sense are presented. Last, two numerical examples are provided to demonstrate the effectiveness of the obtained results by resorting to LMI software package of MATLAB, and the graphical representation is used to explain our results.4. For impulsive neural networks model with unbounded time-varying delays and nonlinear perturbations (?)By constructing reasonable Lyapunov-Krasovski functional and using the analysis theory, we give some LMI conditions forμ-stability neural networks. Two numerical examples are given to illustrate the effectiveness of our results.5. Construct gene regulatory network by time series data of gene expression. First, we reasonably simplified and assumed our model. We assumed that the changing of state variable of each gene is linear relationship with all gene state variable. By this linear relationship, we built gene regulatory network model in linear differential equations. According to time-series data with noise, we optimize the model parameters in Ramsay's algorithm. We explained that this algorithm is feasible in theory. Both in data fitting form and in the equation fitting form, the objective function of Ramsay's algorithm can be written in the form of the sum of square, so we can iterative the MATLAB program in Gauss-Newton algorithm.