OP-II-3

PP-I-9respectively, characterize the rates, activation energies, and heats of F 1 → F 2 andF 2 → F 1 phase transitions; and s is a parameter characterizing the heat-exchangeintensity with the environment.Mathematical model (2) + (3) is a set of two differential equations withcharacteristic nonlinearities (4). In combustion theory and theoretical foundations ofchemical reactors, such a model is a conventional subject of parametric analysis[5–12]. Model (2) + (3) is specific in that it refers a non-flow-through system andcontains two exponents (4), considerably supplementing the variety of the dynamicand nonlinear properties of the system as shown in our earlier investigations. Here,we report the parametric analysis of dynamic system (2) + (3), including analysis ofthe number and steadiness of steady states, the construction of parametricdependences of steady-state characteristics, design of parametric and phaseportraits, and calculations of temporal dependences characterized by dynamic burstsand undamped concentration and temperature oscillations.To summarize, dynamic model (2) + (3) can be regarded as the simplest basicmodel of a first-order phase transition. The parametric analysis of this model showsthat it can have one, three, or five steady states. The parameter regions have beenfound where auto-oscillations exist in a dynamic system; characteristic parameterand phase portraits have been designed for the mathematical model. The processdynamics in the vicinity of a phase transition point can be rather complex. Itscharacteristic features can be hysteresis of temperature dependences, undampedtemperature and concentration oscillations, and considerable dynamic bursts as thesystem tends to acquire a steady state.References[1]. Bykov, V.I. and Tsybenova, S.B., Gorenie Plazmokhim., 2007, vol. 5, no. 1/2, pp. 120–155.[2]. Bykov, V.I. and Tsybenova, S.B., Dokl. Phys. Chem., 2000, vol. 374, nos. 4–6, pp. 196–199[Dokl. Akad. Nauk, 2000, vol. 374, no. 5, pp. 640–643].[3]. Bykov, V.I. and Tsybenova, S.B., Fiz. Goreniya Vzryva, 2001, vol. 37, no. 5, pp. 36–48.[4]. Bykov, V.I. and Tsybenova, S.B., Teor. Osn. Khim. Technol., 2003, vol. 37, no. 1, pp. 64–75.[5]. Bykov, V.I., Tsybenova, S.B., and Slin’ko, M.G., Dokl. Phys. Chem., 2001, vol. 378, nos. 1–3, pp.134–137 [Dokl. Akad. Nauk, 2001, vol. 378, no. 2, pp. 214–217].[6]. Bykov, V.I., Tsybenova, S.B., and Slin’ko, M.G., Dokl. Phys. Chem., 2001, vol. 378, nos. 1–3, pp.138–141 [Dokl. Akad. Nauk, 2001, vol. 378, no. 3, pp. 355–358].[7]. Bykov, V.I., Modelirovanie kriticheskikh yavlenii v khimicheskoi kinetike (Modeling of CriticalPhenomena in Chemical Kinetics), Moscow: Editorial URSS, 2007.AcknowledgementsThis work was supported by the Federal Agency of Education of the Russian Federationin the frame of the Targeted Analytical Program “Development of the Scientific Potential ofHigher Education Institutions for 2009–2010” (project no. 2.1.1/2104).236