With the outbreak of COVID-19 epidemic, the atmospheric NO₂ emission has decreased sharply. This led to the reduction of O₃ level in urban area of Zhangjiajie, but the increase of it in the suburban National Forest Park. Therefore, this study mainly aims to reveal the different responses dynamic mechanism of atmospheric O₃ concentration changes to the sharp reduction of NO₂ pollution in different ecological function areas of Zhangjiajie during the epidemic period (March 1-May 31, 2020) by Multifractal detrended cross-correlation analysis (MFDCCA) and self-organized critical theory (SOC). Based on the hourly average concentration data of NO₂ and O₃ at three monitoring stations in Zhangjiajie (Weiyang Road, Yongding New District, and Yuanjiajie) during the epidemic period (March 1-May 31, 2020) and non-epidemic period (March 1-May 31, 2019), the MFDCCA was used to analyze the multi-scale characteristics of the cross-correlation between NO₂ and O₃. The results indicated that the cross-correlation between NO₂ and O₃ at each station had strong long-term persistence characteristics and multi-fractal characteristics. The long-term persistence of the cross-correlation between NO₂ and O₃ increased by 19.4% on average, and the multi-fractal decreased by 5.7% on average, which was mainly related to the change of atmospheric chemical reaction of O₃ caused by the centralized emission reduction of NO₂ during the COVID-19 epidemic control period. Furthermore, SOC was applied to analyze the macro dynamic mechanism of long-term persistence for cross-correlation between NO₂ and O₃. The results showed that the evolution of O₃ at the Yuanjiajie station was in a self-organized critical state, and the SOC intrinsic dynamic mechanism was an important nonlinear dynamic mechanism that led to the increase of O₃ concentration in Zhangjiajie National Forest Park during the epidemic. However, the O₃ evolution of Weiyang Road and Yongding New Area stations did not yet reach the self-organized critical state, and was only in a subcritical state. This was also the main reason for the decrease of O₃ concentration at urban stations. Accurate identification of the self-organized critical characteristics in O₃ evolution is of great significance for risk assessment for the generation of high O₃ concentrations, and it helps to scientifically assess the impact of human tourism activities on the forest ecosystem.