The Hopfield network (Hopfield, 1982,1984) provides a simple model of an associative memory in a neuronal structure. This model, however, is based on highly artificial assumptions, especially the use of formal-two state neu-rons (Hopfield, 1982) or graded-response neurons (Hopfield, 1984). \Vhat happens if we replace the formal neurons by 'real' biological neurons? \Ve address this question in ...

A model of neurons with hysteresis (or hysteresis binary neurons) for the Hopfield neural networks is studied. We prove theoretically that the emergent collective properties of the original Hopfield neural networks also are present in the Hopfield neural networks with hysteresis binary neurons. As an example, the networks are also applied to the maximum cut problem and results of computer simul...

It is shown that conventional computers can be exponentiallx faster than planar Hopfield networks: although there are planar Hopfield networks that take exponential time to converge, a stable state of an arbitrary planar Hopfield network can be found by a conventional computer in polynomial time. The theory of 'P.cS-completeness gives strong evidence that such a separation is unlikely for nonpl...

This paper investigates some properties of Takagi-Sugeno (T-S) fuzzy Hopfield neural networks. First, we prove that there exists a unique solution of the T-S fuzzy Hopfield neural network. Second, we determine a condition for input-to-state stability (ISS) of the T-S fuzzy Hopfield neural network. These results will be useful to analyze dynamic behavior of fuzzy neural networks.

The information capacity of general forms of memory is formalized. The number of bits of information that can be stored in the Hopfield model of associative memory is estimated. It is found that the asymptotic information capacity of a Hopfield network of N neurons is of the order N3 b. The number of arbitrary state vectors that can be made stable in a Hopfield network of N neurons is proved to...

We introduce a novel type of neural network, termed the parallel Hopfield network, that can simultaneously effect the dynamics of many different, independent Hopfield networks in parallel in the same piece of neural hardware. Numerically we find that under certain conditions, each Hopfield subnetwork has a finite memory capacity approaching that of the equivalent isolated attractor network, whi...

In this paper, we propose a continuous hysteresis neurons (CHN) Hopfield neural network architecture for efficiently solving crossbar switch problems. A Hopfield neural network architecture with continuous hysteresis and its collective computational properties are studied. It is proved theoretically and confirmed by simulating the randomly generated Hopfield neural network with CHN. The network...

The two well-known neural network, Hopfield networks and Radial Basis Function networks, have different structures and characteristics. Hopfield neural network and RBF neural network are two of the most commonly-used types of feedback networks and feedforward networks respectively. This study gives an overview for Hopfield neural network and RBF neural network in architectures, the learning pro...