Criteria for Hopf Bifurcations with Fixed Multiplicities
Pages 147 - 154
Abstract
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.
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