In this paper, we report an open system consisting of three self-replicating peptides, in which peptide 1 inhibits the duplex template of peptide 2, peptide 2 inhibits duplex 3, and peptide 3 inhibits duplex 1 to complete the negative feedback loop. This interacting chemical network yields oscillations in the concentrations of all species over time and establishes a possible mechanism for pre-biotic chemical systems organization. The first focus of our analysis is the effect of altering rates of duplex formation and inhibition on oscillations. We then examine the autocatalytic rate constant in the symmetric and asymmetric cases.