累积放电模型及其符号动力学研究

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

基于累积释放模型提出了一种累积放电模型.相比于累积释放模型,累积放电模型无须变化的阈值调制,即可出现多种状态,例如混沌态、锁频等.利用符号动力学对其进行研究,发现在一定的参数条件下,模型的输出符号序列可以被用于监测模型参数的变化,而且与神经系统的测量相似,都具有很高的分辨率.计算机仿真和电路实验得到的结果也验证了上述说法.电路实验结果显示模型的输出符号序列对输入频率的分辨率最高可以达到0.05Hz,对电流幅值的分辨率可达到1μA,并且都具有很大的动态范围.

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 1μA.