Research On Multistability Of Neural Network

After people have become more and more clear of the biological brain,they began to use a variety of mathematical models to simulate the biological brain.Neural network is an ideal model,which has achieved good results in many practical problems.The stability of neural networks is an important research focus,because stable networks mean that the trajectory from a certain field eventually converges to some attractors,therefore,the stability is an important property in engineering applications.In this thesis,the multistability of neural networks is studied from two aspects of theory and application,and the following research results are obtained:Firstly,we study the multistability of two-dimensional linear threshold recurrent neural networks.In this part,we transform the two-dimensional nonlinear network into a linear network,and use the eigenvalues of the matrix to study the multi-stability of the neural network.The conditions for the coexistence of continuous attractors in the network with external input and the network without external input are obtained respectively.In this part,the multistability of a real connection matrix network with complex eigenvalues is also studied,and the validity of the conclusion is verified by simulation.Secondly,we establish a denoising autoencoder network,complete the access of multiple numbers,and multiple continuous attractors exist in one network,which expands the storage capacity of the network.The rotating picture data set is used to learn the continuous attractor of the rotating picture data set in two and three dimensional space by autoencoder.Finally,the structure of long-short time memory neural network model is built,and the processes of forward propagation and error back propagation are deduced.The memory ability of this model in long series problems is analyzed,and the model is used to predict the time series data(the close price of bitcoin in the past 6 years).Finally,the powerful memory function of the network is verified.To sum up,the above results can promote the research of neural network.