کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639916 1341253 2011 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Zero-Hopf bifurcation for van der Pol’s oscillator with delayed feedback
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Zero-Hopf bifurcation for van der Pol’s oscillator with delayed feedback
چکیده انگلیسی

In this paper, we study the dynamical behaviors of the following van der Pol oscillator with delay ẍ+ε(x2−1)ẋ+x=εg(x(t−τ)). In the case that its associated characteristic equation has a simple zero root and a pair of purely imaginary roots (zero-Hopf singularity), the normal form is obtained by performing a center manifold reduction and by using the normal form theory developed by Faria and Magalhães. A critical value ε0ε0 of εε in (0,2) is obtained to predict the bifurcation diagrams from which saddle–node bifurcation, pitchfork bifurcation, Hopf bifurcation (the existence and stability of the periodic solutions), and heteroclinic bifurcation are determined. Some examples are given to confirm the theoretical results.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 8, 15 February 2011, Pages 2586–2602
نویسندگان
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