As a typical highly nonlinear medium, laboratory plasmas can exhibit abundant nonlinear phenomena. It is well known that the presence of negative differential conductivity can cause the system to exhibit temporal chaotic oscillations when a DC glow discharge is operated in the subnormal glow discharge regime. In addition, for a nonlinear system, the hysteresis often occurs due to the coexistence of multiple attractors. In this work, a two-dimensional plasma fluid model based on the drift-diffusion approximation is developed to study the hysteresis phenomenon of the nonlinear dynamical behaviors of the low-pressure DC glow discharge. The results demonstrate that the initial discharge conditions selected in calculations will influence the nonlinear dynamical behaviors significantly that the system exhibits. Hysteresis can be observed from the voltage waveform when the applied voltage is altered to allow the system to work between the stationary discharge regime and the oscillatory discharge regime. In the hysteresis region, the system exhibits bi-stable characteristics. Near the critical point, the dynamical behaviors of the system will jump from the stationary state to the oscillatory state under small perturbations and the reverse adjustment of control parameters will not immediately restore the original stationary state, which is a typical characteristic of the subcritical Hopf bifurcation.

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