Exploring Intermittent Dynamics of Neural Activity in a Single-Pair System of Excitatory and Inhibitory Neurons

A long-tailed property has been observed at various levels of the brain, ranging from neural population activity to the level of cognitive neurodynamics. Specifically, at the cognitive neurodynamics level, a phenomenon called perceptual alternation displays perceptual durations that follow a gamma or log-normal distribution. Moreover, this perceptual alternation becomes nondeterministic. The occurrence of alternation phenomena has also been noticed in neural populations at the cognitive neurodynamics level. Even in a system consisting of a single pair of excitatory and inhibitory neurons, referred to as chaos-chaos intermittency (CCI), a similar intermittent alternation of neural activity emerges, involving intermittent transitions between multiple isolated attractors. In this study, our hypothesis was that nondeterminism and long-tailed properties can emerge in this single-pair system. To test this hypothesis, we evaluated the determinism of two types of dynamics in the system that couples excitatory and inhibitory neurons: 1) transitions between attractors and 2) behavior within attractors. This evaluation was performed on multiple time scales using multi-scale entropy analysis (MSE) and an iterated amplitude-adjusted Fourier transform (IAAFT) surrogate. The results demonstrated that the transitions between attractors were nondeterministic, while the behavior within attractors was deterministic. Furthermore, a long-tailed property manifested in the duration of the transitions between attractors, possibly resulting from long-term evaluation in the chaotic unstable orbit. The emergence of this long-tailed property was attributed to the low frequency CCI around the attractor-merging bifurcation. This discovery contributes to the understanding of the long-tailed properties exhibited by neural activity across multiple levels.