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二维1:-5 Lotka-Volterra复四次系统的可线性化条件
胡召平,张超
作者单位E-mail
胡召平 上海大学 理学院, 上海 200444 zhaopinghu@shu.edu.cn 
张超 上海大学 理学院, 上海 200444  
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
=x(1-a30x3-a21x2y-a12xy2-a03y3),=-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)
Linearizability conditions for 1:-5 Lotka-Volterra two-dimensional complex quartic systems
Hu Zhaoping,Zhang Chao
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 = x(1-a30x3-a21x2y-a12xy2-a03y3), =-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