Criteria for Hopf Bifurcations with Fixed Multiplicities
Criteria for Hopf Bifurcations with Fixed Multiplicities
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DOI：
10.1145/3452143.3465519
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Ryoya Fukasaku
中科院分区：
文献类型：
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作者：
Ryoya Fukasaku
Hopf分岔定理利用特殊坐标下的先验假设，给出了poincar<s:1> - andronov -Hopf分岔存在的充分条件。在2020年，Kruff和Walcher引入了一种有用的方法来计算简单poincar<s:1> - andronov - hopf分岔的充分条件，而不需要这样的先验假设。本文针对多个Hopf分岔，推广了该方法。作者在计算机代数系统SageMath上实现了这种广义方法。通过实例说明了广义方法的有效性。
The Hopf bifurcation theorem gives us a sufficient condition for that there is a Poincaré-Andronov-Hopf bifurcation by using prior assumptions on special coordinates. In 2020, Kruff and Walcher introduced a useful method to compute sufficient conditions for simple Poincaré-Andronov-Hopf bifurcations without such prior assumptions. In the paper, for multiple Hopf bifurcations, we generalize the method. The author has implemented the generalized method on the computer algebra system SageMath. The usefulness of the generalized method is illustrated by the implementation.