Xie ZK, Fan WC, Wang QA (2000b) 'Comparative studies on catastrophe dynamics of ignition phenomena - Part II.' (Chemical Industry Press: Beijing) 791-799

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Abstract: Thermal explosion behavior of open-flow system involves with many important applied fields of industry such as chemical reactor, rocket and jet engine, and combustion stove. The introduced bifurcation theory and the presentation of the unity theory between thermal explosion and chain reaction one promote the development of thermal explosion remarkably. For combustible ignition problems, comparing with the bifurcation theory, the catastrophe theory is provided with some features, for instance, brevity, well-bedded classification method, and well to describing multi-parameters ignition system ill visual ways. It is of more advantages to integrate realize and cross-link lots of discontinuity behaviors happening in varying ignition system, starting from catastrophic mode which can describe the global characteristics of system. The catastrophe theory is more robust especially when the investigating system is a kind of incomplete system, where types and number of control variables are not clearly or imperfectly to be realized and expressed. Here, as it is hard to determine the perfect governing equations of the system, whether the bifurcation theory or the other quantitative mathematical tools is impossible to be applied to. Thermal explosion behaviors of open-flow system are also a kind of typical discontinuous phenomena. It has important significance to realize the thermal explosion laws happening in open-flow system by means of the catastrophe set, catastrophe mode and the acting relations between the control variables and the catastrophe mode. The thermal explosion behavior of first-order adiabatic CSTR System also has cusp catastrophe mechanism, and therefore is provided with some features such as kicking, hysteretic, bimodal, inaccessibility and divergence, and so on, too.