TY - GEN
T1 - Criteria for Hopf Bifurcations with Fixed Multiplicities
AU - Fukasaku, Ryoya
N1 - Funding Information:
This work was supported by KAKENHI 20K19745.
Publisher Copyright:
© 2021 ACM.
PY - 2021/7/18
Y1 - 2021/7/18
N2 - 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.
AB - 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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U2 - 10.1145/3452143.3465519
DO - 10.1145/3452143.3465519
M3 - Conference contribution
AN - SCOPUS:85111076894
T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
SP - 147
EP - 154
BT - ISSAC 2021 - Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation
PB - Association for Computing Machinery
T2 - 46th International Symposium on Symbolic and Algebraic Computation, ISSAC 2021
Y2 - 18 July 2021 through 23 July 2021
ER -