کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4629865 | 1340587 | 2012 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The 1: −q resonant center problem for certain cubic Lotka–Volterra systems
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Necessary conditions and distinct sufficient conditions are derived for the system x˙=x(1-a20x2-a11xy-a02y2), y˙=y(-q+b20x2+b11xy+b02y2) to admit a first integral of the form Φ(x,y)=xqy+⋯Φ(x,y)=xqy+⋯ in a neighborhood of the origin, in which case the origin is termed a 1:-q1:-q resonant center. Necessary and sufficient conditions are obtained for odd q,q⩽9q,q⩽9; necessary conditions, most of which are also sufficient, are obtained for even q,q⩽8q,q⩽8. Key ideas in the proofs are computation of focus quantities for the complexified systems and decomposition of the variety of the ideal generated by an initial string of them to obtain necessary conditions, and the theory of Darboux first integrals to show sufficiency.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 218, Issue 23, 1 August 2012, Pages 11620–11633
Journal: Applied Mathematics and Computation - Volume 218, Issue 23, 1 August 2012, Pages 11620–11633
نویسندگان
Xingwu Chen, Jaume Giné, Valery G. Romanovski, Douglas S. Shafer,