کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898769 | 1631498 | 2018 | 51 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A proof of Wright's conjecture
ترجمه فارسی عنوان
مدرک حدس رایت
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
Wright's conjecture states that the origin is the global attractor for the delay differential equation yâ²(t)=âαy(tâ1)[1+y(t)] for all αâ(0,Ï2] when y(t)>â1. This has been proven to be true for a subset of parameter values α. We extend the result to the full parameter range αâ(0,Ï2], and thus prove Wright's conjecture to be true. Our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at α=Ï2. This analysis fills the gap left by complementary work on Wright's conjecture, which covers parameter values further away from the bifurcation point. Furthermore, we show that the branch of (slowly oscillating) periodic orbits originating from this Hopf bifurcation does not have any subsequent bifurcations (and in particular no folds) for αâ(Ï2,Ï2+6.830Ã10â3]. When combined with other results, this proves that the branch of slowly oscillating solutions that originates from the Hopf bifurcation at α=Ï2 is globally parametrized by α>Ï2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 12, 15 June 2018, Pages 7412-7462
Journal: Journal of Differential Equations - Volume 264, Issue 12, 15 June 2018, Pages 7412-7462
نویسندگان
Jan Bouwe van den Berg, Jonathan Jaquette,