Stability Analysis Of Two Kinds Of Neural Networks Based On Fixed Point Theory

Neural network is a new interdisciplinary subject and an important part of artificial intelligence research,which has become the focus of brain science,neuroscience,computer science,mathematics,cognitive science,physical science,psychology and other disciplines.Because of its strong association ability,fault tolerance and self-adaptability,the system can solve many practical problems in pattern recognition,signal processing and image processing.As a typical nonlinear system,the stability of neural network is one of its most important dynamic characteristics.In this thesis,the stability of cellular neural networks and gene regulatory networks is studied by virtue of fixed point theory.The main contents are as follows:First of all,the research background and development status of neural network stability are shown,which provide a correct direction for the work of this thesis.Secondly,the problem of the mean square exponential stability of a class of impulsive stochastic reaction-diffusion cellular neural networks(CNNs)with transmission delays and distributed delays,and parameter uncertainties is discussed.By using H?lder inequality,It? isometric nature and Contraction Mapping Principle,a sufficient condition to guarantee the mean square exponential stability of the above CNNs is proposed,and a specific example is given to verify the effectiveness of the obtained results.Last but not least,the problem of globally stochastically exponential stability in the pth moment for a class of T-S fuzzy stochastic impulsive genetic regulatory networks with random discrete delays,distributed delays and parameter uncertainties is studied.By utilizing the theory of stochastic analysis,semigroup theory and fixed point theory,a novel sufficient condition to guarantee the globally stochastically exponential stability in the pth moment of the considered genetic regulatory networks is derived,and a specific example is given to show the result is effective.