Department of Mathematics, Building 303S, Technical University of Denmark, 2800 Lyngby, Denmark.
J Chem Phys. 2011 Apr 14;134(14):144105. doi: 10.1063/1.3577998.
Templators are differential equation models for self-replicating chemical systems. Beutel and Peacock-López [J. Chem. Phys. 126, 125104 (2007)] have numerically analyzed a model for a cross-catalytic self-replicating system and found two cases of canard explosion, that is, a substantial change of amplitude of a limit cycle over a very short parameter interval. We show how the model can be reduced to a two-dimensional system and how canard theory for slow-fast equations can be applied to yield analytic information about the canard explosion. In particular, simple expressions for the parameter value where the canard explosion occurs are obtained. The connection to mixed-mode oscillations also observed in the model is briefly discussed.
模板是自我复制化学系统的微分方程模型。Beutel 和 Peacock-López [J. Chem. Phys. 126, 125104 (2007)] 已经对交叉催化自复制系统的模型进行了数值分析，并发现了两种奇异吸引子爆炸的情况，即在非常短的参数间隔内，极限环的幅度发生了实质性的变化。我们展示了如何将模型简化为二维系统，以及如何应用慢-快方程的奇异吸引子理论来获得关于奇异吸引子爆炸的解析信息。特别是，得到了奇异吸引子爆炸发生时参数值的简单表达式。还简要讨论了该模型中观察到的混合模式振荡的联系。
