Various applications of volume dielectric barrier discharges (DBDs) with airflows have attracted significant attention such as in the fields of plasma medicine, surface modification, ozone synthesis, etc. In this work, the nonlinearity characteristics of DBDs in initiating and extinguishing boundaries with airflows are experimentally investigated. It is found that the difference between initiating pulse repetition frequencies (PRFs) and extinguishing PRFs is affected by the addition of airflows. A hysteresis region is produced between these two PRFs. A topological rule of Thom’s classification theorem is proposed to investigate the hysteresis phenomenon of discharges with airflows. It is concluded that the discharge state is dependent on the operation route. The discharge state would transit from initiating to extinguishing, or in the opposite direction, while passing along a specific operation route. Based on the topological method, two nonlinear laws of discharge structure transition under the typical operation routes are predicted and verified in the discharge experiments.

体积介质阻挡放电（DBDs）在气流中的各种应用引起了人们的广泛关注，例如在等离子体医学、表面改性、臭氧合成等领域。在这项工作中，DBDs在起爆和熄灭气流边界方面的非线性特性是实验研究。发现启动脉冲重复频率 (PRF) 和熄灭 PRF 之间的差异受气流增加的影响。在这两个 PRF 之间产生一个滞后区。提出了 Thom 分类定理的拓扑规则来研究气流放电的滞后现象。结论是放电状态取决于操作路线。放电状态由起爆过渡到熄灭，或相反方向，同时沿特定运营路线行驶。基于拓扑方法，在放电实验中预测并验证了典型运行路线下放电结构转变的两条非线性规律。