کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9501611 1338757 2005 54 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
چکیده انگلیسی
We analyze homoclinic orbits near codimension-1 and -2 heteroclinic cycles between an equilibrium and a periodic orbit for ordinary differential equations in three or higher dimensions. The main motivation for this study is a self-organized periodic replication process of travelling pulses which has been observed in reaction-diffusion equations. We establish conditions for existence and uniqueness of countably infinite families of curve segments of 1-homoclinic orbits which accumulate at codimension-1 or -2 heteroclinic cycles. The main result shows the bifurcation of a number of curves of 1-homoclinic orbits from such codimension-2 heteroclinic cycles which depends on a winding number of the transverse set of heteroclinic points. In addition, a leading order expansion of the associated curves in parameter space is derived. Its coefficients are periodic with one frequency from the imaginary part of the leading stable Floquet exponents of the periodic orbit and one from the winding number.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 218, Issue 2, 15 November 2005, Pages 390-443
نویسندگان
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