کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4630103 1340593 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bifurcation of local critical periods in the generalized Loud’s system
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Bifurcation of local critical periods in the generalized Loud’s system
چکیده انگلیسی

We study the bifurcation of local critical periods in the differential systemx˙=-y+Bxn-1y,y˙=x+Dxn+Fxn-2y2,where B,D,F∈RB,D,F∈R and n ⩾ 3 is a fixed natural number. Here by “local” we mean in a neighbourhood of the center at the origin. For n even we show that at most two local critical periods bifurcate from a weak center of finite order or from the linear isochrone, and at most one local critical period from a nonlinear isochrone. For n odd we prove that at most one local critical period bifurcates from the weak centers of finite or infinite order. In addition, we show that the upper bound is sharp in all the cases. For n = 2 this was proved by Chicone and Jacobs in [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Am. Math. Soc. 312 (1989) 433–486] and our proof strongly relies on their general results about the issue.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 218, Issue 12, 15 February 2012, Pages 6803–6813
نویسندگان
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