95-10-093
Abstract:
Chaotic Interactions of Self-Replicating RNA
Chrisitan V. Forst
A general system of high-order differential equations describing
complex dynamics of replicating biomolecules is given. Symmetry
relations and coordinate transformations of general replication
systems leading to topologically equivalent systems are derived.
Three chaotic attractors observed in Lotka-Volterra equations of
dimension n=3 are shown to represent three cross-sections of one
and the same chaoatic regime. Also a fractal torus in a generalized
three-dimensional Lotka-Volterra Model has been linked to
one of the chaotic attractors. The strange attractors are studied
in the equivalent four-dimensional catalytic replicator network.
The fractal torus has been examined in adapted Lotka-Volterra equations.
Analytic expressions are derived for the Lyapunov exponents of the
flow in the replicator system. Lyapunov spectra for different pathways
into chaos has been calculated. In the generalized Lotka-Volterra
system a second inner rest point---coexisting with (quasi)-periodic
orbits---can be observed; with an abundance of different bifurcations.
Pathways from chaotic tori, via quasi-periodic tori, via limit
cycles, via multi-periodic orbits---emerging out of periodic
doubling bifurcations---to "simple" chaotic attractors can be found.
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