کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4632910 | 1340657 | 2009 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study the analytic system of differential equations in the plane which can be written, in a suitable coordinates system, as(xË,yË)T=âi=0âFq-p+2is,where p,qâN,p⩽q,s=(n+1)p-q>0,nâN and Fi=(Pi,Qi)T are quasi-homogeneous vector fields of type t=(p,q) and degree i, with Fq-p=(y,0)T and Qq-p+2s(1,0)<0. The origin of this system is a nilpotent and monodromic isolated singular point. We show the Taylor expansion of the return map near the origin for this system, which allow us to generate small amplitude limit cycles bifurcating from the critical point. Also, as an application of the theoretical procedure, we characterize the centers and we generate limit cycles of small amplitude from the origin of several families. Finally, we give a new family integrable analytically which includes the centers of the systems studied.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 215, Issue 1, 1 September 2009, Pages 314-323
Journal: Applied Mathematics and Computation - Volume 215, Issue 1, 1 September 2009, Pages 314-323
نویسندگان
A. Algaba, C. GarcÃa, M. Reyes,