We show that a unit-grup, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclie connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-grup has the dynamics such that the amount n of units which belong to the unit-grup increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-grups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.

In order to introduce the burst firing, a nerve-cell dynamic feature, we extend the Inverse function Delayed model (ID model), which is the neuron model with ability to oscillate and has powerful ability on the information processing. This dynamics is discussed for the relation with the functional role of the brain and is characterized by repeated patterns of closely spaced action potentials. It is expected that the additional new characteristics add extra functions to neural networks. Using the relation between the ID model and reduced Hodgkin-Huxley model, we propose the neuron model with ability of burst. The proposed model excelled the ID model in solving the N-Queen problem. Additionally, the prototype chip for the burst ID model is implemented and measured.