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Hopf bifurcation in 3-dimensional polynomial vector fields
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2021-10-06 , DOI: 10.1016/j.cnsns.2021.106068 Iván Sánchez-Sánchez 1 , Joan Torregrosa 1, 2
中文翻译:
3 维多项式向量场中的 Hopf 分岔
更新日期:2021-11-04
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2021-10-06 , DOI: 10.1016/j.cnsns.2021.106068 Iván Sánchez-Sánchez 1 , Joan Torregrosa 1, 2
Affiliation
In this work we study the local cyclicity of some polynomial vector fields in In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. All limit cycles are small amplitude limit cycles and bifurcate from a Hopf type equilibrium. We introduce how to find Lyapunov constants in for considering the usual degenerate Hopf bifurcation with a parallelization approach, which enables to prove our results for 4th and 5th degrees.
中文翻译:
3 维多项式向量场中的 Hopf 分岔
在这项工作中,我们研究了一些多项式向量场的局部循环性 特别地,我们给出了具有 11 个极限环的二次系统、具有 31 个极限环的三次系统、具有 54 个极限环的四次系统和具有 92 个极限环的五次系统。所有的极限环都是小振幅极限环并且从 Hopf 型平衡分叉。介绍如何求李雅普诺夫常数 考虑使用并行化方法的通常退化 Hopf 分岔,这能够证明我们的 4 度和 5 度结果。