A recurrent neural network with serial delay elements for memorizing limit cycles

A recurrent neural network (RNN), in which each unit has serial delay elements, is proposed for memorizing limit cycles (LCs). This network is called DRNN in this paper. An LC consists of several basic patterns. The hysteresis information of LCs, realized on the connections from the delay elements to the units, is very efficient in the following reasons. First, the same basic patterns can be shared by different LCs. This make it possible to drastically increase the number of LCs, even though using a small number of the basic patterns. Second, noise performance, that is, probability of recalling the exact LC starting from the noisy LC, can be improved. The hysteresis information consists of two components, the order of the basic patterns included in an LC, and the cross-correlation among all the basic patterns. The former is highly dependent on the number of LCs, and the latter the number of all the basic patterns. In order to achieve good noise performance, a small number of the basic patterns is preferred. These properties of the DRNN are theoretically analyzed and confirmed through computer simulations. It is also confirmed that the DRNN is superior to the RNN without delay elements for memorizing LCs