Study of an integrate-and-discharge model with symbolic dynamics

Abstract

An integrate-and-discharge model (IDM) is proposed on the basis of an integrate-and-fire model (IFM). Compared with the IFM, the IDM can obtain rich dynamic information including chaos, phase locking, etc., without using varying threshold modulation. The corresponding relation between output symbolic sequences and parameters (i.e., frequency, amplitude, resistance and capacity) of the IDM is established by using symbolic dynamics. Moreover, a method of obtaining symbolic sequence as well as an ordering rule is presented. Simulation and circuit experiment validate the correctness of the method and the rule. The results of circuit experiment show that the frequency resolution can reach up to 0.05 Hz in some frequency ranges and the amplitude resolution can reach up to 1 μA.