This paper reports plasma behavior in an un-magnetized, co-axial electrode geometry DC glow discharge plasma system. Fluctuations and hysteresis in discharge characteristics have been observed when the electrode system has a central anode configuration. The important fact is that fluctuations and hysteresis in discharge characteristics are not observed in a central cathode configuration. The radial profile of plasma potential shows that it is less than the anode potential, so current continuity is maintained in this current-driven system. This paper also attempts to identify the source of order-to-chaos-to-order in floating potential oscillations with respect to the discharge characteristics. When discharge current (Id) increases after the first negative differential resistance region, the system self-organizes and stabilizes into a state of periodic oscillations. Chaotic behavior is a possible development of new dynamical states in the discharge, which develops from an initial high frequency, low amplitude oscillations (in the range 11.6 mA < Id < 15 mA) and, thereafter, transits to low frequency, large amplitude oscillations at Id >15 mA. In the reverse path of discharge characteristics, the oscillations are more regular than in the forward path. Before the production of low frequency, large amplitude oscillations, the current oscillations follow a similar pattern to the floating potential oscillations. As it transits from chaotic to low frequency, large amplitude floating potential oscillations, discharge current oscillations show a chaotic type of behavior.