Study Of An Integrate-and-discharge Model With Symbolic Dynamics

Based on symbolic analysis, a new parameter estimation method of an Integrate-and-Fire model (1FM) is proposed. With varying threshold modulations, the IFM can output many kinds of spike-trains. And their dynamics can be described using circle map. With symbolic dynamics, we can get the symbols of the IFM by directly measuring the phase. Using the formalism of Markov chain, a cost function has been given in this paper to find the optimal parameters of the model. The minimum of this function yields a good estimate for the model parameters. The computer simulations prove that the method is effective even when the symbol sequence is short and corrupted by a significant amount of noise.Then an integrate-and-discharge model (IDM) is proposed based on an integrate-and-fire model (IFM). Compare to the IFM, the IDM can get rich dynamics 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 applied symbolic dynamics. Moreover, a method of obtaining symbolic sequence as well as an ordering rule is presented. Simulation and circuit experiment have validated the method and the rule. The results of circuit experiment show that frequency resolution can reach up to0.05Hz in some frequency ranges and amplitude resolution can reach up to1uA.