In this paper, we first analyze the distribution of local fields (DLF) which is induced by the memory patterns in the Q-Ising model. It is found that the structure of the DLF is closely correlated with the network dynamics and the system performance. However, the design rule adopted in the Q-Ising model, like the other rules adopted for multi-state neural networks with associative memories, cannot be applied to directly control the DLF for a given set of memory patterns, and thus cannot be

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... ed to further study the relationships between the structure of the DLF and the dynamics of the network. We then extend a design rule, which was presented recently for designing binary-state neural networks, to make it suitable for designing general multi-state neural networks. This rule is able to control the structure of the DLF as expected. We show that controlling the DLF not only can affect the dynamic behaviors of the multistate neural networks for a given set of memory patterns, but also can improve the storage capacity. With the change of the DLF, the network shows very rich dynamic behaviors, such as the 'chaos phase', the 'memory phase', and the 'mixture phase'. These dynamic behaviors are also observed in the binary-state neural networks; therefore, our results imply that they may be the universal behaviors of feedback neural networks.