Chaos, intermittency and hysteresis in the dynamic model of a polymerization reactor.

*(English)*Zbl 0744.58047Summary: 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 |

##### Keywords:

polymerization reactor; strange attractor; Poincaré sections; Lyapunov exponents; successive iterate maps; period oscillations; chaos
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\textit{F. Teymour} and \textit{W. H. Ray}, Chaos Solitons Fractals 1, No. 4, 295--315 (1991; Zbl 0744.58047)

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