Numerical Continuation Techniques for Planar Slow-Fast Systems
Numerical Continuation Techniques for Planar Slow-Fast Systems
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DOI：
10.1137/120877386
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发表时间：
2013-01-01
影响因子：
2.1
通讯作者：
Desroches, M.
中科院分区：
文献类型：
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作者：
De Maesschalck, P.;Desroches, M.
已知连续技术成功地描述出现在具有多于一个慢变量的慢-快系统中的分叉图（参见，E。例如，在一个实施例中，[M. Desroches，B. Krauskopf和H. M. Osinga，Nonlinearity，23（2010），pp. 739-765]）。在本文中，我们探讨的有用的数值延拓技术处理一些解决和一些开放的问题在研究平面奇异摄动。更确切地说，我们首先验证已知的理论结果（从而显示这种数值工具的可靠性）的外观上的多个极限环的松弛振荡型和多个临界周期的存在，精心挑选的环中的慢-快周期轨道的平面。然后，我们应用该技术来详细研究周期函数。
Continuation techniques have been known to successfully describe bifurcation diagrams appearing in slow-fast systems with more than one slow variable (see, e. g., [M. Desroches, B. Krauskopf, and H. M. Osinga, Nonlinearity, 23 (2010), pp. 739-765]). In this paper we investigate the usefulness of numerical continuation techniques dealing with some solved and some open problems in the study of planar singular perturbations. More precisely, we first verify known theoretical results (thereby showing the reliability of this numerical tool) on the appearance of multiple limit cycles of relaxation-oscillation type and on the existence of multiple critical periods in well-chosen annuli of slow-fast periodic orbits in the plane. We then apply the technique to study the period function in detail.