The origin of adaptation and dyssymmetry in the evolution of autocatalytic systems

The evolution of open systems that include several autocatalytic processes in parallel or in series is mathematically analyzed. For the case of two reactions in parallel, such systems progressively and finally select the reaction pathway which involves the better autocatalyst. The effect of parameters influencing the rate of this evolution is discussed. Where catalysts are strictly equivalent, e.g. enantiomers in a symmetrical surrounding, the evolution is amplified by fluctuations and retains finally only one reaction pathway, if the autocatalytic rates of reactions are more than proportional to the catalyst concentrations. When including two reactions in series, these open systems are also able to give oscillations.