| 摘要: |
本文考虑了如下的一类平面四次复Lotka-Volterra系统的可线性化问题
ẋ=x（1-a30x3-a21x2y-a12xy2-a03y3）,ẏ=-y（5-b30x3-b21x2y-b12xy2-b03y3）.
该系统为四次齐次多项式扰动下的具有$1:-5$线性项的复Lotka-Volterra系统，给出了该系统可线性化的充分必要条件. |
| 关键词: 多项式系统 可线性化 不变曲线 余因式 |
| DOI：10.3969/J.ISSN.100-5137.2017.03.014 |
| 分类号: |
| 基金项目:This research was supported by the Natural Science Foundation of China (No. 11401366, 11632008) |
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| Linearizability conditions for 1:-5 Lotka-Volterra two-dimensional complex quartic systems |
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Hu Zhaoping, Zhang Chao
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College of Sciences, Shanghai University, Shanghai 200444, China
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| Abstract: |
| In this paper we investigate the linearizability problem for the planar Lotka-Volterra complex quartic systems which are 1:-5 linear systems perturbed by homogeneous polynomials of degree 4, that is to say, we consider systems of the form ẋ = x(1-a30x3-a21x2y-a12xy2-a03y3), ẏ =-y(5-b30x3-b21x2y-b12xy2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found. |
| Key words: polynomial systems linearization invariant curve cofactor |
