Chemical Oscillations

Rebek has synthesized self-replicating molecules in the laboratory. Given the importance of such molecules, we are introducing a simple model of self-replicating molecules for the first time. The model mimics the experimental template mechanism and is an important new dynamical model with cubic nonlinearity. This nonlinearity is modeled after the self-replicating mechanism recently reported in the literature. Here we consider the full templator model and a minimal model, which disregard the uncatalyzed step in the mechanism. For the minimal model, we find an exact analytical expression for the locations of the bifurcation points. For the full model, however, we obtain analytical approximations for the bifurcation points that compare very well with the exact numerical solutions.