Couple, double, toil and trouble: Dynamic behavior of coupled oscillatory reacting systems.

摘要

This thesis presents a computational study of the dynamic behavior of several models describing two coupled chemical reactors. Attention is focussed on the case where the behavior of both--not necessarily identical--reactors is oscillatory when uncoupled. The effects of systematically varying two parameters have been investigated: (a) the strength of the coupling between the two reactors, and (b) the difference between the "natural" states of the systems when they are uncoupled. Emphasis is placed on the way the dynamic behavior develops with increasing coupling strength from the asymptotic limit of weak coupling where the behavior can be deduced from that of the individual reactors. These detailed two-parameter studies provide a coherent framework in which many previous experimental and computational studies can be consistently integrated. The scenario of common dynamic features which emerges is independent of the order of the reaction, whether the reaction is isothermal or catalytic, the details of the mechanism, or the particular form of the coupling. For weak coupling, an interplay between quasiperiodicity and resonance is observed. This resembles the behavior observed in periodically forced oscillators. Indeed, the entire structure of resonance regions and the breaking of quasiperiodic solutions as the coupling strength increases appears to be a common feature of coupled reacting systems and coupled oscillators in general. The phenomenon of mutual extinction of oscillations which has been observed in previous experimental and one-parameter computational studies has been confirmed and characterized as an integral piece of this two-parameter framework. The examples studied include chemical reactions in both isothermal and nonisothermal coupled CSTRs, a microbial predator-prey interaction in coupled chemostats and a chemical reaction occurring on catalytic surfaces coupled through the gas phase.