Negative differential resistance, instability, and critical transition in lightning leader

The phenomena of leader extinction and restrike during lightning events, such as multiple strokes in ground flashes or recoil leaders in cloud flashes, present significant challenges. A key aspect of this issue involves the discussion of the channel's negative differential resistance and its instability. From the perspective of bifurcation theory in nonlinear dynamics, this paper suggests an inherent consistency among the channel's negative differential resistance, channel instability, and critical transition from insulation to conduction. This study examines the differential-resistance characteristics of the leader-streamer system in lightning development. We correlate the differential-resistance characteristics of the leader-streamer channel with the channel's state and instability transitions, investigating the critical current and potential difference conditions required for the stable transition of the leader-streamer channel.