A generalized Lengyel–Epstein oscillating reaction model is proposed and analyzed. The existence of limit cycles is proved using Hopf and Bautin bifurcation theory. We analyze the dynamics of the well known chlorine dioxide–iodine–malonic acid reaction, using a differential equations system. The numerical results are shown and these agree with the experimental data reported in the literature. We found that the oscillatory behavior depends on the stoichiometric coefficients and the reactant concentrations. This work gives valuable information for applications like design, optimization, dynamics and control of the industrial chemical reactors.

中文翻译：

---

广义 Lengyel-Epstein 系统中的 Hopf 和 Bautin 分岔

提出并分析了广义的 Lengyel-Epstein 振荡反应模型。使用Hopf 和Bautin 分岔理论证明了极限环的存在。我们使用微分方程系统分析了众所周知的二氧化​​氯-碘-丙二酸反应的动力学。显示了数值结果，这些结果与文献中报道的实验数据一致。我们发现振荡行为取决于化学计量系数和反应物浓度。这项工作为工业化学反应器的设计、优化、动力学和控制等应用提供了有价值的信息。