Seminaris en biofísica/biomatemática, 12 de Novembre, 12:30, Aula S.1 EPSEB

Josep Sardanyés
Complex Systems Lab (ICREA - Universitat Pompeu Fabra)
Parc de Recerca Biomèdica de Barcelona (PRBB-GRIB)

The hypercycle: insights into the origin of life problem through nonlinear dynamical systems

The hypercycle, which was proposed by Manfred Eigen and Peter Schuster in the 1970's, is a network of catalytically-coupled replicators and has been suggested to explain key steps in prebiotic evolution. This system allows to overcome the information crisis of error prone replicators with quasispecies distribution. By means of mathematical models based on nonlinear differential equations and cellular automata (CA) models we analyze the asymptotic dynamics and bifurcation scenarios of simple symmetric and asymmetric hypercycles. We show the presence of a saddle-node bifurcation governing the extinction scenario and involving the "appearance" of a ghost in the phase plane which delays the flows towards the extinction attractor.   Homologous to the saddle-node bifurcation, the CA shows that the extinction phase is governed by an absorbing first-order phase transition. We also analyze the same system considering a weak parasite i.e., a replicator that receives catalysis but does not provide catalytic aid to any other hypercycle member. It is shown that the presence of the parasite can trigger the appearance of self-organizing spatial patterns and of chaotic dynamics governed by fractal attractors.