TY - GEN
T1 - Using Symbolic Computation to Analyze Zero-Hopf Bifurcations of Polynomial Differential Systems
AU - Huang, Bo
N1 - Publisher Copyright:
© 2023 ACM.
PY - 2023/7/24
Y1 - 2023/7/24
N2 - This paper is devoted to the study of infinitesimal limit cycles that can bifurcate from zero-Hopf equilibria of differential systems based on the averaging method. We develop an efficient symbolic program using Maple for computing the averaged functions of any order for continuous differential systems in arbitrary dimension. The program allows us to systematically analyze zero-Hopf bifurcations of polynomial differential systems using symbolic computation methods. We show that for the first-order averaging, ĝ.,"ĝ {0, 1, ..., 2n - 3} limit cycles can bifurcate from the zero-Hopf equilibrium for the general class of perturbed differential systems and up to the second-order averaging, the maximum number of limit cycles can be determined by computing the mixed volume of a polynomial system obtained from the averaged functions. A number of examples are presented to demonstrate the effectiveness of the proposed algorithmic approach.
AB - This paper is devoted to the study of infinitesimal limit cycles that can bifurcate from zero-Hopf equilibria of differential systems based on the averaging method. We develop an efficient symbolic program using Maple for computing the averaged functions of any order for continuous differential systems in arbitrary dimension. The program allows us to systematically analyze zero-Hopf bifurcations of polynomial differential systems using symbolic computation methods. We show that for the first-order averaging, ĝ.,"ĝ {0, 1, ..., 2n - 3} limit cycles can bifurcate from the zero-Hopf equilibrium for the general class of perturbed differential systems and up to the second-order averaging, the maximum number of limit cycles can be determined by computing the mixed volume of a polynomial system obtained from the averaged functions. A number of examples are presented to demonstrate the effectiveness of the proposed algorithmic approach.
KW - Algorithmic approach
KW - averaging method
KW - limit cycles
KW - symbolic computation
KW - zero-Hopf bifurcation
UR - https://www.scopus.com/pages/publications/85167822313
U2 - 10.1145/3597066.3597114
DO - 10.1145/3597066.3597114
M3 - 会议稿件
AN - SCOPUS:85167822313
T3 - ACM International Conference Proceeding Series
SP - 307
EP - 314
BT - ISSAC 2023 - Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation
A2 - Jeronimo, Gabriela
PB - Association for Computing Machinery
T2 - 48th International Symposium on Symbolic and Algebraic Computation, ISSAC 2023
Y2 - 24 July 2023 through 27 July 2023
ER -