Xie ZK, Fan WC, Wang QA (2000a) 'Comparative studies on catastrophe dynamics of ignition phenomena - Part I.' (Chemical Industry Press: Beijing) 784-790

Web link:

Keywords:

Abstract: The unity of gradual change and catastrophe is one of the essential characteristics of motions in objective world system. The catastrophe theory and catastrophe classification theorem open out the common mathematical essence of discontinuity behaviors from more comprehensive meaning, and provide the basis for integrating understanding discontinuity behaviors widely existing in objective world. An igniting -quenching behavior is also typical catastrophe phenomenon. In the phase space of dynamical system formed by igniting system, a change of system state, form, and structural stability is mapped onto the change of phase point in phase space. By the study on catastrophe dynamics of an ignition system, the catastrophe mode and catastrophe set of the system may be found out, and the mechanism of an igniting-quenching behaviors, catastrophe critical condition and controlling ways (catastrophe controlling) may be analyzed. And the igniting-quenching characteristics, catastrophe mode and the commonness features of different igniting system may be comparatively studied on the basis of catastrophe classification. The uniform temperature and non-adiabatic Semenov System is of the cusp catastrophe mechanism. Beside the known hysteretic nature, the system is also of some other features such as kicking, bimodal, inaccessibility and divergence.