Chemical oscillations and Turing patterns in a generalized two-variable model of chemical self-replication

Chemical self-replication of oligonucleotides and helical peptides show the so-called square root rate law. Based on this rate we extend our previous work on ideal replicators to include the square root rate and other possible nonlinearities, which we couple with an enzimatic sink. Although the nonlinearity is necessary for complex dynamics, the nature of the sink is the essential feature in the mechanism that allows temporal and spatial patterns. We obtain exact general relations for the Poincare-Adronov-Hopf and Turing bifurcations, and our generalized results include the Higgins, autocatalator, and templator models as specific cases.