Notice of RetractionThe eqviualence of fuzzy logical dynamics and the neural circuits' dynamics

In order to probe the secret of our brain, it is necessary to design large scale dynamical neural circuits( more than 106 neurons) to simulate complex process of our brain. But such kind task is not easy to achieve only based on the analysis of partial equations especially for complex neural models, e.g. Rose-Hindmarsh (RH) model. So we should develop a novel approach which combines logic and machine learning in the designation or analysis of large scale neural circuits, and this new approach should be able to greatly simplify the designation of large scale dynamical neural circuits which is really very important both for cognition science and neural science. For this purpose, we introduce the concept of fuzzy logical framework of a neural circuit, and we proved that if the behave of a neural circuit can be described by first order partial differential equations, then such kind neural circuit can be simulated with arbitrary small errors by a Hopfield neural circuit which has a uniform structure or a fuzzy logical dynamical system; for more, a novel learning approach for large scale layered neural circuits based on PSVM and back propagation is developed for training Hopfield neural circuits.