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Chaos, intermittency and hysteresis in the dynamic model of a polymerization reactor. (English) Zbl 0744.58047
Summary: Experimental evidence of sustained oscillatory behavior for a lab-scale polymerization reactor was presented previously, and confirmed in modelling studies. A modified mathematical model for this process describing full scale reactors was later analyzed in detail. Bifurcation theory and numerical continuation techniques were used in locating complex dynamic structures. Results pointed to the possibility of chaotic behavior in the dynamics of the model analyzed. This paper is aimed at a more detailed investigation of the chaotic regime. The structure of the strange attractor is first illustrated and characterized using different methods (e.g. Poincaré sections, Lyapunov exponents, successive iterate maps,…). Numerical experiments in the chaotic regime are then conducted. These reveal the presence of numerous periodic windows with odd period oscillations; in some cases, chaos is seen to disappear and re-emerge through the intermittency mechanism. Also a mechanism of chaotic transition through hysteresis and preperiodicity is observed and is shown to be related to a tangent bifurcation similar to that leading to intermittency. It is believed to constitute a possible new universal route to the emergence of chaos.

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
82D60 Statistical mechanical studies of polymers
82D75 Nuclear reactor theory; neutron transport
58Z05 Applications of global analysis to the sciences
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