کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4620140 1339455 2009 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Characterizing isochronous points and computing isochronous sections
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Characterizing isochronous points and computing isochronous sections
چکیده انگلیسی

We consider two-dimensional autonomous systems of differential equationsx˙=−y+λx+P(x,y),y˙=x+λy+Q(x,y), where λ is a real constant and P and Q are smooth functions of order greater than or equal to two. These systems, so-called centre-focus type systems, have either a centre or a focus at the origin. We characterize the systems with a weak isochronous focus at the origin by means of their radial and azimuthal coefficients. We prove, in this case, the existence of a normalized vector field and an isochronous section which arrives at the origin with defined direction. We also provide algorithms that compute the radial and azimuthal coefficients, terms of normalized vector field and of isochronous section of a system. As applications, we analyze the weak isochronous foci for quadratic systems and for systems with cubic non-linearities, and we give a three-parameter family of Rayleigh equations with four local critical periods.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 355, Issue 2, 15 July 2009, Pages 564–576
نویسندگان
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