Nonlinear behavior of glow discharge plasmas is experimentally investigated. The glow is generated between a barrier semiconductor electrode, Chromium doped namely Gallium Arsenide (GaAs: Cr), as a cathode and an Indium-Tin Oxide (ITO) coated glass electrode as an anode, in reverse bias. The planar nature of electrodes provides symmetry in spatial geometry. The discharge behaves oscillatory in the time domain, with single and sometimes multiperiodicities in plasma current and voltage characteristics. In this paper, harmonic frequency generation and transition to chaotic behavior is investigated. The observed current-voltage characteristics of the discharge are discussed in detail.