کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
759357 | 896474 | 2010 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On cascades of bifurcations leading to chaos in several nonlinear dissipative systems of ODEs On cascades of bifurcations leading to chaos in several nonlinear dissipative systems of ODEs](/preview/png/759357.png)
This paper considers several nonlinear dissipative systems of ordinary differential equations. The studied systems undergo a full analysis of corresponding singular points on a whole set of parameters’ values variation. Specifically, types of singular points, boarders of stability regions, as well as presented local bifurcations, are determined. By using numerical methods a consideration of scenarios of transition to chaos in these systems with one bifurcation parameter variation is held. The aim of this research is a confirmation of a Feigenbaum–Sharkovskii–Magnitskii mechanism of transition to chaos unique for all dissipative systems of ODEs. As the result of analysis of one of the systems the lack of any chaotic behavior is shown with the help of Poincare sections.
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 15, Issue 10, October 2010, Pages 2974–2986