| This thesis addresses a number of topics in the study and analysis of the dynamics of chemical reactions and reactors, with particular emphasis on surface catalyzed reactions. The influence of recent developments in the theory of dynamical systems is apparent both in the choice of problem, and in the techniques developed and applied in their solution. The scope of these techniques, conversely, extends to fields beyond chemical dynamics.; In the first two chapters a study of the dynamics of single species surface reactions is presented. It is shown that a multivalued adsorption isotherm is necessary to predict rate oscillations. The questions of uniform solution stability, phase separation, surface coupling and nonlinear surface diffusion arise then naturally, and are discussed and generalized.; The necessity of good qualitative understanding of the dynamics of coupled chemical oscillators are stressed in the above problem. A useful first step in this direction is the study of periodically forced systems, and the remaining chapters deal with the study of such systems. The stroboscopic phase plane is introduced and illustrated as a convenient approach that facilitates the analysis of forced systems both conceptually and computationally.; An algorithm for the computation of invariant circles, tori and invariant manifolds in general is developed and illustrated. An extensive study of periodically forced chemical oscillators follows, with emphasis on common qualitative features in their behavior for small and intermediate forcing amplitudes.; A detailed two-parameter study of the forced CSTR follows, and a part of its excitation diagram is presented; this diagram shows qualitative changes in the system behavior as a function of the amplitude and the frequency of the forcing. The continuation of perturbation low amplitude results to intermediate and high forcing amplitude reveals several codimension two bifurcations and stresses the necessity for algorithms to locate global bifurcations. One such algorithm is briefly described.; Finally, the structure of some resonance regions for periodically forced oscillators is examined, and this leads to some conjectures on frequency locking for coupled oscillators in general. |
