Mathematical Modeling of Continuous Diene Polymerization Based on a System of Differential Equations

Title	Mathematical Modeling of Continuous Diene Polymerization Based on a System of Differential Equations
Authors	B. L. Khashper¹, D. S. Yunusova¹, E. R. Gizzatova¹ ¹Yugra State University
Annotation	This study investigates the continuous polymerization of dienes using Ziegler-Natta catalysts. A mathematical model of the process was developed based on a system of differential equations describing the dynamics of reagent concentration changes. The analysis included examination of the partial derivatives matrix characterizing each components contribution to the reaction rate. The eigenvalues of this matrix were calculated and analyzed, revealing key patterns of the polymerization process. The developed methodology was successfully tested on experimental polymerization data.
Keywords	polymerization, chemical kinetics, system of differential equations, rate matrix, matrix eigenvalues.
Citation	Khashper B. L., Yunusova D. S., Gizzatova E. R. ''Mathematical Modeling of Continuous Diene Polymerization Based on a System of Differential Equations'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 263-268. Available at: https://conf.svmo.ru/files/2025/papers/paper53.pdf. - Date of access: 30.08.2025.