Mixed-mode oscillations in a self-replicating dimerization mechanism

Abstract

Recently, self-replicating molecules have been synthesized in the laboratory by Rebek. Given the importance of such molecules, we proposed a simple model of a self-replicating dimer, which works as a template for its own formation. Here we consider a three variable model. For the model, we obtain mixed-mode and chaotic oscillations. Also, we find coexistence between two periodic attractors as well as a periodic and a chaotic attractor.