The Research On Synchronization Of Two Class Of Neural Networks With Discontinuous Activation Functions

At present, many areas of human life have been tied up with artificial intelligence, such as speech recognition, rescue robot, image recognition, etc. Artificial intelligence can be re-garded as a fresh intelligence machine, like human being, who is capable to deal with some complex affairs. Intelligent machines must be studied as neural network models like human brain. Some researchers have found that the form of information transmission between neu-rons is discontinuous, and synapses between transmitters can appear delay phenomenon in many realistic neural networks. So, it is important to study the neural network with discontin-uous activation functions and time delay. In this paper, we introduce the synchronization in two class of neural networks with discontinuous activation functions and time-varing delays. The main contents and conclusions of this dissertation are shown in details as below:Because the neural network model with discontinuous activations can better describe some natural phenomenons, global exponential synchronization for a class of delayed fuzzy cellular networks with discontinuous activations is investigated in this paper. Unlike the methods in the existing literatures, we introduce some new results of exponential synchro-nization by utilizing Lyapunov stability theory and under the framework of Filippov solution. Especially, the paper successfully avoids the strict limits on activation functions in some lit-eratures. Finally, the numerical simulations of two examples are introduced to further show the reasonableness of the design strategy in this thesis.On the other hand, through the analysis of the present situation of researches on com-petitive neural network, we find that many literatures on synchronization of the competi-tive neural network rarely consider discontinuous activations, time-varying delays and the finite-time synchronization at the same time. Motivated by some recent works, in this case, we discuss the finite-time synchronization for a class of competitive neural networks with discontinuous activations and time-varying delays. In order to realize finite-time synchro-nization for the competitive neural networks, we design a controller. However, in order to enlarge the applications of synchronization method, we further simplify the controller in this paper. By means of Lyapunov function and its stability theory, we rigorously prove that the controllers can make trajectory errors stable at the origin between the drive and response net-works synchronized in theory. At last, we use the numerical simulations of two illustrative examples to show the reasonableness of the design method.