A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks. A symbolic representation of the dynamics in this equation is given as a directed graph on an N-dimensional hypercube. This provides a formal link with discrete neural networks such as the original Hopfield models. Analytic criteria are given to establish steady states and limit cycle osci...

DOWNLOAD http://bit.ly/1OslRBc Artificial neural networks: theory and applications This comprehensive tutorial on artifical neural networks covers all the important neural network architectures as well as the most recent theory-e.g., pattern recognition, statistical theory, and other mathematical prerequisites. A broad range of applications is provided for each of the architectures. Artificial ...

From the mathematical point of view, an artificial neural network corresponds to a nonlinear transformation of some inputs into certain outputs. Many types of neural networks have been proposed and studied in the literature and the Hopfield-type network has become an important one due to its potential for applications in various fields of daily life. A neural network is a network that performs ...

Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of scientific investigation. As for the research branch, neural networks are handled and studied by psychologists, neurobiologists, engineers, mathematicians and theoretical physicists. In particular, in theoretical physics...

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference control system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method.

⎯The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of th...

This paper discusses the implementation of Hopfield neural networks for solving constraint satisfaction problems using Field Programmable Gate Arrays (FPGAs). It discusses techniques for formulating such problems as discrete neural networks, and then it describes the N-Queen problem using this formulation. A prototype implementation of the a number of different NQueen problems is described and ...

The Hopfield neural networks and the holographic neural networks are models which were successfully simulated on conventional computers. Starting with these models, an analogous fundamental quantum information processing system is developed in this article. Neuro-quantum interaction can regulate the ”collapse”-readout of quantum computation results. This paper is a comprehensive introduction in...

Inspired by biological neuronal systems, artificial neural networks have demonstrated superior characteristics of learning, adaptation, classification and function-approximation. They have been successfully applied to many areas. However, conventional neural networks are feed-forward networks that move the information in only one direction, forward, from the inputs to the outputs. There are no ...