کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840573 908484 2012 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Reversible periodic orbits in a class of 3D continuous piecewise linear systems of differential equations
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Reversible periodic orbits in a class of 3D continuous piecewise linear systems of differential equations
چکیده انگلیسی

The so-called noose bifurcation is an interesting structure of reversible periodic orbits that was numerically detected by Kent and Elgin in the well-known Michelson system. In this work we perform an analysis of the periodic behavior of a piecewise version of the Michelson system where this bifurcation also exists. This variant is a one-parameter three-dimensional piecewise linear continuous system with two zones separated by a plane and it is also a representative of a wide class of reversible divergence-free systems.In the piecewise system, the noose bifurcation involves reversible periodic orbits that intersect the separation plane at two or four points. This work is focused on those reversible periodic orbits that intersect the separation plane twice (RP2-orbits). It is established that for every TT between 2π2π and a critical point, there exists a unique value of the parameter for which the system has an RP2-orbit with period TT. Moreover, this critical value, that separates periodic orbits with two or four points of intersection with the separation plane, corresponds to an RP2-orbit that crosses the separation plane tangentially.It is also proved that in a parameter versus period bifurcation diagram, the curve of this family of periodic orbits has a unique maximum point, which corresponds to the saddle-node bifurcation of periodic orbits that appears in the noose bifurcation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 15, October 2012, Pages 5866–5883
نویسندگان
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