The motivation for this report is to examine a Hydrogen Peroxide oscillator in the `Primordial Soup' as a driver for RNA self-replication in the RNA World Model and thus offer a possible explanation to the origins of life. To do this I aim to replicate and verify the model Professor Rowena Ball and Professor. John Brindley produced in their paper `Hydrogen peroxide thermo-chemical oscillator as driver for primordial RNA replication' [2] and to expand further upon their results by examining a two-pore model system. This paper also aims to prove certain results in the study of dynamical systems for my own personal interest. I would like to thank my supervisors Professor Mark Nelson and Professor Rowena Ball, without whom this paper would not have been possible.