Temporal nonlinear dynamics control of atmospheric pressure dielectric barrier discharge based on data-driven methods

The temporal nonlinear dynamics of atmospheric pressure dielectric barrier discharge (DBD) poses a critical challenge in stabilizing the discharge mode. While ppm-level impurities can modulate the discharge, conventional numerical simulations struggle to efficiently determine doping content for mode transitions. Here, we combine a one-dimensional plasma fluid model with a data-driven framework that integrates feature dimensionality reduction and interpolation prediction to reveal the regulation mechanism of nitrogen content on the discharge mode in helium DBD. These results show that regardless of whether the initial discharge is chaotic, period-multiplying, or asymmetric single-period, the discharge behavior follows a common evolution with increasing nitrogen content: first entering or maintaining a chaotic state, then undergoing inverse period-doubling bifurcation, and finally stabilizing into a single-period mode. Moreover, the proposed quantitative criterion based on the discharge mode number M successfully determines the nitrogen content boundaries for mode transitions under different initial conditions. The predicted modes agree well with those calculated through the plasma model. Overall, this work provides both theoretical insight into the stability control of weakly ionized plasma fluids and a practical predictive tool for achieving stable, uniform atmospheric pressure DBDs through ppm-level impurity content.