CHAOTIC INTERACTIONS OF SELF-REPLICATING RNA

A general system of high-order differential equations describing compl ex dynamics of replicating biomolecules is given. Symmetry relations a nd coordinate transformations of general replication systems leading t o topologically equivalent systems are derived. Three chaotic attracto rs observed in Lotka-Volterra equations of dimension n = 3 are shown t o represent three cross-sections of one and the same chaotic regime. A lso a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange at tractors are studied in the equivalent four-dimensional catalytic repl icator network. The fractal torus has been examined in adapted Lotka-V olterra equations. Analytic expressions are derived for the Lyapunov e xponents of the Row in the replicator system. Lyapunov spectra for dif ferent pathways into chaos has been calculated. In the generalized Lot ka-Volterra system a second inner rest point-coexisting with (quasi)-p eriodic orbits-can be observed; with an abundance of different bifurca tions. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits-emerging out of periodic doubling bi furcations-to ''simple'' chaotic attractors can be found.