Complex dynamics in a cross-catalytic self-replication mechanism.

The authors consider a minimal cross-catalytic self-replicating system of only two cross-catalytic templates that mimics the R3C ligase ribozyme system of Dong-Eu and Joyce [Chem. Biol. 11, 1505 (2004)]. This system displays considerably more complex dynamics than its self-replicating counterpart. In particular, the authors discuss the Poincare-Andronov-Hopf bifurcation, canard transitions, excitability, and hysteresis that yield birhythmicity between simple and complex oscillations.