关于无ε系统中鸭式爆炸点的近似
On the approximation of the canard explosion point in epsilon-free systems
摘要：
鸭式爆炸是指非线性常微分方程系统的极限环的周期和振幅在一个很窄的分岔参数区间内发生的剧烈变化。它发生在慢-快系统中，并且在奇异扰动问题中得到很好的理解，其中小参数ε定义了时间尺度分离。本文提出了一种确定鸭式布局爆炸点的迭代算法，该算法适用于一般的慢-快系统，且不需要明确的小参数。我们还提出了假设下，该算法给出了准确的估计鸭爆炸点。最后，将该算法应用于van der Pol方程组和一个无显式小参数的自复制系统的Templator模型，得到了与数值模拟结果非常一致的结果.
英文摘要：
A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of non-linear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow-fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines the time scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow-fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion point. Finally, we apply the algorithm to the van der Pol equations and a Templator model for a self-replicating system with no explicit small parameter and obtain very good agreement with results from numerical simulations.
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