Complex Periodic and Chaotic States in Heterogeneous Catalytic Systems
Zioudas, Anthony Philip
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https://hdl.handle.net/2142/66644
Description
Title
Complex Periodic and Chaotic States in Heterogeneous Catalytic Systems
Author(s)
Zioudas, Anthony Philip
Issue Date
1980
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
Simple theoretical models were developed accounting for usual kinetic and transport processes occurring in gas solid-catalyzed reactions to explain experimentally observed complex, self-generated, sustained dynamic behavior.
The devised heterogeneous chemical oscillators were capable of exhibiting a range of dynamical behavior. This range included stable steady states, single-peak and multi-peak periodic oscillations, and also choatic behavior.
The three ordinary differential equations models answered the puzzling question as to whether the experimentally observed complex dynamics is inherent in the equartions of the proposed models rather than being caused by random influences or caused by processes of which no knowledge exist at the present.
The chaotic states appeared for a short range of parameters after a finite cascade of bifurcations which led the system from single-, to two-, to three-, to four-, to six-, to eight-peak periodic oscillations and ultimately to chaotic states.
The trajectories in phase space and Poincare surface of sections for the chaotic states exhibited "strange attractor" features.
The linearized analysis of the models led to the conclusion that the strange behavior is associated with the presence of three eigenvalues, one simple negative and two complex conjugate which just cross the imaginary axis to the right of the complex plane. From this analysis, the conjecture was made by invoking Hopf's bifurcation theorem that the differential flow is on a conic surface.
The heterogeneous chemical oscillators had common features with the Lorenz oscillator in the sense that the maximums in the three dimensions had maps similar to the Lorenz maps.
A version of the models generated by a two-dimensional oscillator molded on the manifold with multiplicity developed chaotic oscillations.
The isothermal versions of the models, being two-dimensional systems, were capable of exhibiting oscillatory behavior of single-peak periodic type.
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