鞍型慢流形的迭代法计算
Computation of saddle type slow manifolds using iterative methods
摘要：
本文提出了一种计算鞍型慢流形上轨迹段的方法。这种方法是基于迭代法，而不是搭配型方法。与需要网格细化以确保关于$ε$的一致收敛性的配置法相比，使用本文的方法可以直接获得适当的估计。该方法适用于几个例子，包括：一对神经元耦合的相互抑制与两个慢，两个快的变量和计算的同宿连接的FitzHugh-Nagumo系统。
英文摘要：
This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $ε$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.
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