The critical avalanche of an excitation–inhibition neural network composed of Izhikevich neurons is studied based on the bifurcation of the mean-field

In recent years, there has been significant interest in exploring how the brain efficiently propagates and processes information. When the system is in a critical state, it may have preferable information transmission, calculation, and processing abilities, so the study of this state has attracted wide attention. Here, we primarily focus on the excitation–inhibition (E–I) neural network composed of Izhikevich neurons and the derived accurate mean-field model. To understand the critical neuronal avalanche more comprehensively and deeply, we consider the spike characteristics of individual neurons (spike or burst firing), the criticality of neural networks, and the bifurcations of the mean-field. It is observed that no matter the spike or burst firing, near different bifurcations of the mean-field, the neural network appears in phase transition and the neuronal avalanche satisfies the critical condition. In other words, the bifurcation of this mean-field model can more accurately and conveniently predict the occurrence of critical avalanches, thus narrowing the detection range. These findings contribute to a deeper understanding of critical avalanches. By establishing the relationship between the spike of individual neurons, microscopic neural network, and macroscopic mean-field, new insight is provided into the dynamic origin of critical neuronal avalanches.