一类三维Jerk系统的余维二Bautin分岔分析
Research on Codimensional-2 Bautin Bifurcation of a Three-Dimensional Jerk System
DOI: 10.12677/pm.2025.1511270, PDF,    国家自然科学基金支持
作者: 陈玉明：赣南师范大学，数学与计算机科学学院，江西 赣州
关键词: Hopf分岔；Bautin分岔；Jerk系统；Hopf Bifurcation； Bautin Bifurcation； Jerk System
摘要: 针对一类具有三次项的三维Jerk系统，本文致力于分析该系统的余维二Bautin分岔行为。首先，基于Hopf分岔理论，给出了Hopf分岔发生的适当参数条件，并计算了相对应的第一Lyapunov系数；其次，研究了Hopf分岔发生退化后的余维二Bautin分岔行为，给出了对应的分岔参数条件，并计算了第二Lyapunov系数；最后，通过数值仿真，对Bautin分岔平衡点进行了适当的参数扰动，获得了分岔后的不同动力学行为。
Abstract: This paper is devoted to analyzing the codimension-2 Bautin bifurcations of a generalized three-dimensional (3D) jerk system which is jerk function with some cubic terms. First, some adequate parameter conditions for guaranteeing the occurrence of Hopf bifurcation of this jerk system are given, and the first Lyapunov coefficient is obtained. Second, some adequate parameter conditions for guaranteeing the occurrence of Bautin bifurcation of this jerk system are given, and the second Lyapunov coefficient is obtained. Finally, according to the theoretical analyses and numerical simulation, under some certain parameter conditions, the above theoretical analyses are verified.
文章引用：陈玉明. 一类三维Jerk系统的余维二Bautin分岔分析[J]. 理论数学, 2025, 15(11): 76-84. https://doi.org/10.12677/pm.2025.1511270

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