Simulation of a Chaos-Like Irregular Neural Firing Pattern Based on Improved Deterministic Chay Model

Abstract

In this paper, the deterministic Chay model was improved considering the generation mechanism of an action potential, with special relevance to the opening of potassium channel after depolarization. Then a chaos-like irregular non-periodic neural firing pattern, which was lying between period n and period (n + 1) bursting in a period-adding bifurcation and composed of alternating period n and period (n + 1) bursts, was also simulated by this improved Chay model. The nonlinear time series analysis results suggest this pattern display both deterministic and stochastic dynamic characteristics, as same as those results in the previous studies. This pattern was always simulated by stochastic neuron models and considered to be coherence resonance near the bifurcation points induced by the inner noise. However, there was no noise in this improved deterministic Chay model. This present paper attempted to discuss and preliminarily explain the generation mechanism of this firing pattern from the standpoint of the unification of certainty and randomness.