کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840208 1470518 2013 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bautin bifurcation in a delay differential equation modeling leukemia
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Bautin bifurcation in a delay differential equation modeling leukemia
چکیده انگلیسی

This paper continues the work contained in two previous papers of the authors, devoted to the qualitative study of the dynamical system generated by a delay differential equation that models leukemia. The problem depends on five parameters and has two equilibria. As already known, at the non-zero equilibrium solution, for certain values of the parameters, Hopf bifurcation occurs.Our aim here is to investigate the Bautin bifurcation for the considered model. By using a second order approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points. We explore the space of parameters in a zone of biological interest and find, by direct computation, points where the first Lyapunov coefficient equals zero. These are candidates for Bautin type bifurcation. For these points we compute the second Lyapunov coefficient, that determines the type of Bautin bifurcation. The computation of the second Lyapunov coefficient requires a fourth order approximation of the center manifold, that we determine. The points with null first Lyapunov coefficient obtained are given in tables and are also plotted on surfaces of Hopf bifurcation obtained by fixing two parameters. Next we vary two parameters around a point in the space of parameters with l1=0l1=0 and numerically explore the behavior of the solution. The results confirm the Bautin type-bifurcation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 82, April 2013, Pages 142–157
نویسندگان
, ,