The Stability Analysis And Control Of Fractional Order BAM Neural Networks

Neural network,as one of the hot spots in the research of nonlinear systems,has an irreplaceable role in the understanding of human beings and discovery the laws of nature.In recent years,more and more scholars use fractional calculus to improve the existing neural networks,so that the network models have higher accuracy.There have been successful cases in the field of dynamic systems,biopharmaceutical and artificial intelligence,etc.Based on the original BAM neural network model,we reconstruct three kinds of Caputo type fractional order BAM neural networks,which are extended from the integer order to fractional ord er.By using the stability theory of fractional order nonlinear systems,we analyze the stability of the models and its control models,and the conclusions are verified to be valid by MATLAB programming.The main works of this paper are as follows:A class of Caputo type fractional order BAM neural network model is constructed.If satisfying certain inequal conditions,the system has at least one equilibrium point.Then by establishing a Lyapunov function,and using matrix inequality method and Laplace transform method,we find that the model at equilibrium point is globally asymptotically stable.Finally,the impulsive model is proved to be globally Mittag-Leffler stable.N umerical simulations show that the conclusions are effective.A class of Caputo type different fractional orders BAM neural network model is constructed.By using contraction mapping principle,sufficient conditions for the existence of a unique equilibrium point are obtained.Then we use Laplace transform method and the related theorem of Mittag-Leffler function to get the result of global asymptotic stability of this model.The model added with adaptive feedback control is proved to be globally asymptotically stable by the same method,and the stability criterions are proved true by programming.A class of Caputo type fractional order BAM neural network model with delays is constructed.If the parameters of the system satisfy theorem 5.1,the equilibrium po int of the model exists only.The global asymptotic stability of the model at the equilibrium point is obtained by the fractional comparison principle with delays and the fractional Lyapunov stability theorem with delays.Finally,by designing a fractional order sliding surface and controller,the error control system is proved to be asymptotically stable,and the numerical simulation results are significant.