On the examples of frontal polymerization, tumor growth, and propagation of the nerve impulse, we examined nonlinear phenomena in chemistry and biology. The results of theoretical and experimental studies on the loss of stability of thermal waves of frontal polymerization were presented. The stationarity loss limits for the reactions of epoxide resin curing, polymerization of metal-containing acrylamide complexes, and copolymerization of methyl methacrylate and styrene in the presence of single-walled nanotubes were experimentally studied and theoretically calculated. It was shown that stability of the frontal process waves depends on the heat balance of the exothermic polymerization reaction. Nonlinear phenomena at variation of the polymerization kinetic parameters were studied. The limits of the transition from stationary to nonstationary mode were determined on the basis of experimental data and theoretical calculations. Theoretical study of a diffusion-kinetic model of tumor growth was discussed; the wave nature of the propagation of tumors was shown. The FitzHugh–Nagumo model was studied in view of the diffusion equation; the possibility of formation of the oscillatory modes during the nerve impulse propagation was demonstrated.

中文翻译：

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自动波模式下发生的化学和生物过程之间的类比

在额叶聚合，肿瘤生长和神经冲动传播的例子中，我们研究了化学和生物学中的非线性现象。给出了正面聚合热波稳定性损失的理论和实验研究结果。通过实验研究和理论计算了环氧树脂固化，含金属的丙烯酰胺络合物的聚合以及甲基丙烯酸甲酯和苯乙烯在单壁纳米管存在下的共聚反应的平稳损失极限。结果表明，正面过程波的稳定性取决于放热聚合反应的热平衡。研究了聚合动力学参数变化的非线性现象。根据实验数据和理论计算确定了从平稳模式过渡到非平稳模式的极限。讨论了肿瘤生长扩散动力学模型的理论研究；显示了肿瘤传播的波特性。根据扩散方程研究了FitzHugh–Nagumo模型。证明了在神经冲动传播过程中形成振荡模式的可能性。