Version 1
: Received: 17 April 2024 / Approved: 17 April 2024 / Online: 17 April 2024 (12:03:23 CEST)
How to cite:
Lu, J.; Huang, W.; Wang, Q. Center and Hopf Bifurcation of High-order Singularity in a Class of Three-dimensional Systems. Preprints2024, 2024041149. https://doi.org/10.20944/preprints202404.1149.v1
Lu, J.; Huang, W.; Wang, Q. Center and Hopf Bifurcation of High-order Singularity in a Class of Three-dimensional Systems. Preprints 2024, 2024041149. https://doi.org/10.20944/preprints202404.1149.v1
Lu, J.; Huang, W.; Wang, Q. Center and Hopf Bifurcation of High-order Singularity in a Class of Three-dimensional Systems. Preprints2024, 2024041149. https://doi.org/10.20944/preprints202404.1149.v1
APA Style
Lu, J., Huang, W., & Wang, Q. (2024). Center and Hopf Bifurcation of High-order Singularity in a Class of Three-dimensional Systems. Preprints. https://doi.org/10.20944/preprints202404.1149.v1
Chicago/Turabian Style
Lu, J., Wentao Huang and Qinlong Wang. 2024 "Center and Hopf Bifurcation of High-order Singularity in a Class of Three-dimensional Systems" Preprints. https://doi.org/10.20944/preprints202404.1149.v1
Abstract
This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.
Keywords
high-order degenerate singularity; singular point value; limit cycle; center condition
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
