Convergence Analysis of Hopfield Neural Networks

84 Abstract—In this paper, we analyze the convergence and stability properties of Hopfield Neural Networks (HNN). The global convergence and asymptotic stability of HNN have successful various applications in computing and optimization problems. After determining the mathematical model of the network, we do some analysis on the model. This analysis base on Lyapunov Stability Theorem. Firstly, we define positive definite energy function for the system, then investigate the first derivative of this function. According to the Lyapunov Stability Theorem, the first derivative of function must be negative. We do some mathematical processes while proofing the theorem. At the end, we give a sufficient condition in the Theorem-1 for HNN which guarantees the convergence of the system. We give the definition of Lyapunov Stability Theorem and use it for the proof steps. Finally, we give some simulation results for the globally asymptotically stable system. It can be easily observed that the equilibrium point for the system goes to zero. Derived conditions are also supported by the previous results in the literature and the analyses contribute new sufficient condition to the literature.