Chaotic Neural Network And Its Simple Application

This paper will focus on discussing the three-dimensional Hopfield neural network, based on the theories of delay differential equation, the theories of Hopf bifurcation and the theories of fractional order differential equations,and the methods of controlling chaos and conditions of producing chaos are obtained. Computer simulations are performed to support the theoretical predictions.Main results are as follows:In the third part, the three-dimensional Hopfield neural network with delayed feedback is considered. By employing the theories of delay differential equation to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation and the stability analysis of periodic solutions are given. The application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results by the Matlab software.In the fourth part, the fractional order three-dimensional Hopfield neural network is considered. Based on the theories of fractional order differential equations,the properties of stability and chaos of fractional order three-dimensional Hopfield neural network are considered. According to Rouche's theorem, the condition of producing chaos is obtained. By using predictor-corrector method for numerical computations,some numerical simulations are carried out to illustrate the obtained results that fractional order Hopfield neural network model has more dynamics properties than the integer order.