| Abstract: | A very simple model prebiotic system is explored, both, to elucidate the full complexity of its dynamic behavior, and from the standpoint of what a thermal analysis can tell us about evolution more generally. The system consists of a coacervate containing a four variable enzymatic oscillator that is driven by a single input concentration. The reaction scheme is “nested”; i.e., by “turning on” one reaction at a time we can go from a two‐variable system, to one of three variables, to one of four, each developing more complex behavior. The four‐variable system is shown to have at least five distinct genera of complex attractors within the range examined. Two of these coexist for the same parameter values; the other three are substantially separated in the bifurcation space. The fixed points, characteristic roots, Lyapunov exponents, stability (dissipation), Kaplan‐Yorke dimensions, and correlation dimensions are all calculated for each attractor. A six‐variable amplification of the reaction scheme is considered as a simple model of nucleation in a coacervate and is shown to totally stabilize the corresponding attractor. An Evolutionary Potential is proposed that is wholly beyond the purview of classical thermostatics, yet incorporates entropy effects via Clausius' strong version of the Second Law. It is shown that the latter is a necessary condition for the sort of structuring characteristic of living systems. © 2003 Wiley Periodicals, Inc. Complexity 8: 45–67, 2003 |
