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A one-dimensional numerical simulation of a homogeneous dielectric barrier discharge has been carried out for a nonequilibrium helium-oxygen mixture plasma to understand the influences of oxygen additive on its discharge characteristics at atmospheric pressure. The numerical results obtained by solving continuity equations for plasma species and Poisson equation show that, depending on the amount of oxygen added, the homogeneous barrier discharge turns out to have two fundamental modes: glow and Townsend. When oxygen is rare, the discharge has similar characteristics to the direct current glow discharge at low pressure. As the oxygen additive increases, the discharge characteristics of the glow mode are destroyed and changed into the Townsend mode. The reason for this mode transition is due to the fact that oxygen plays an important role both in quenching helium metastables and in attaching electrons on it in the plasma. As a practical method of sustaining the glow mode even with high oxygen concentration in the discharge, adjustment of the frequency of applied driving voltage is introduced. The numerical simulation reveals that the glow mode recovers from the Townsend mode by increasing the frequency while the amount of oxygen is highly contained. Finally, discharge operation regimes for the glow and Townsend modes are numerically obtained, which are dependent on both oxygen additive and applied frequency.