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Atmospheric-pressure plasma jet presents a good solution as plasma source for many applications in plasma medicine: dermatology, dentistry, cancer treatment, and sterilization or decontamination technologies. The mechanism of discharge generation and propagation in dielectric-barrier helium plasma jet is studied. Trains of spatially localized plasma structures, so-called “plasma bullets,” can be observed at different positions between electrodes or in air. Using ultrafast photography technique, we show that these structures can be homogeneous and nonhomogeneous with respect to the intensity of the emitted light. The nonlinear dynamics analysis applied for the discharge current traces provides us the attractors of the plasma system dynamics in the reconstructed state space.