کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8898826 1631501 2018 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations
ترجمه فارسی عنوان
محدود کردن تعداد سیکل های محدود از سیستم های دیفرانسیل متناوب با استفاده از معادلات پیکارد-فوچ
کلمات کلیدی
چرخه محدودیت سیستم دیفرانسیل متساوی، معادله فوکاس پیکاردا، سیستم دیفرانسیل صاف مستطیلی،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
In this paper, by using Picard-Fuchs equations and Chebyshev criterion, we study the upper bounds of the number of limit cycles given by the first order Melnikov function for discontinuous differential systems, which can bifurcate from the periodic orbits of quadratic reversible centers of genus one (r19): x˙=y−12x2+16y2, y˙=−x−16xy, and (r20): x˙=y+4x2, y˙=−x+16xy, and the periodic orbits of the quadratic isochronous centers (S1):x˙=−y+x2−y2, y˙=x+2xy, and (S2):x˙=−y+x2, y˙=x+xy. The systems (r19) and (r20) are perturbed inside the class of polynomial differential systems of degree n and the system (S1) and (S2) are perturbed inside the class of quadratic polynomial differential systems. The discontinuity is the line y=0. It is proved that the upper bounds of the number of limit cycles for systems (r19) and (r20) are respectively 4n−3(n≥4) and 4n+3(n≥3) counting the multiplicity, and the maximum numbers of limit cycles bifurcating from the period annuluses of the isochronous centers (S1) and (S2) are exactly 5 and 6 (counting the multiplicity) on each period annulus respectively.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 9, 5 May 2018, Pages 5734-5757
نویسندگان
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