Under study is the mathematical model describing the inverse temperature hysteresis as well as the self-sustained oscillations in the CO oxidation over a palladium catalyst in an chemical stirred tank reactor (CSTR). We consider the reaction dynamics under temperature-programmed conditions: At first, the temperature T of the CSTR monotonically increases (due to outside heating) and then it decreases to the initial value. As the temperature goes up, on the surface and in the bulk of the catalyst two palladium oxide forms appear and then, while the temperature decreases, the catalyst reduces to its original state. The mathematical model of nonstatinary processes in such a CSTR is the piecewise continuous system of nonlinear ordinary differential equations (ODE), i.e, a discrete-continuous system. Using the theory of dynamical systems and bifurcation theory as well as numerical methods, we study the structure of the maximal families of the steady states and periodic solutions in dependence on temperature. For the system under study some sufficient conditions are given under which an inverse hysteresis is observed on the dependence of the conversion of the main reagent versus T. Moreover, as temperature decreases, there are self-oscillations of the reaction rate and CO conversion on the lower back branch of the hysteresis. The parameters of the model are found such that the experimental data are qualitatively described.

中文翻译：

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钯在催化CO氧化数学模型中逆滞回的后部支路上的自持振荡

正在研究的是描述化学搅拌釜反应器（CSTR）中逆温度滞后以及钯催化剂上CO氧化中自持振荡的数学模型。我们考虑程序升温条件下的反应动力学：首先，温度TCSTR的值单调增加（由于外部加热），然后减小到初始值。随着温度升高，在催化剂的表面和大部分中会出现两种形式的氧化钯，然后，当温度降低时，催化剂还原到其原始状态。这种CSTR中非平稳过程的数学模型是非线性常微分方程（ODE）的分段连续系统，即离散连续系统。使用动力学系统理论和分叉理论以及数值方法，我们研究了取决于温度的稳态和周期解的最大族的结构。T.此外，当温度降低，有反应速率和CO转化率在滞后的下背部分支的自振荡。找到模型的参数，以便定性描述实验数据。