The Stability Of Hopfield Neural Networks

This dissertation mainly studies the stability of Hopfield Neural Networks and consists of three chapters. In chapter 1, the structure and the parameter of continuous Hopfield Neural Networks are introduced. Then the existence and uniqueness of the balance point is studied with the modern mathematics methods. Finally, the global asymptotic stability of the networks is studied with Lyapunov Direct Method. During the proof, the M-matrix theory is used. In chapter 2, the stability of distributed delayed Hopfield Neural Networks is studied. Firstly, the existence of the balance point is studied with Brouwer Fixed Point Theorem. Then the stability of both constant coefficient distributed delayed Hopfield Neural Networks and variable coefficient distributed delayed Hopfield Neural Networks are studied with Lyapunov Function Method. During the proof, the delayed Halanay differential inequality is used. In chapter 3, the Lyapunov functional based new method is used to study the Delayed Cellular Neural Networks. Then with the same method, both the Delayed Hopfield Neural Networks and Hopfield Neural Networks without delay are studied.