Homoclinic_bif.png
Summary
Description Homoclinic bif.png |
English:
Author: Claire Postlethwaite. Made in xfig. A phase portrait before, at, and after a homoclinic bifurcation in 2D. The periodic orbit grows until it collides with the saddle point. At the bifurcation point the period of the periodic orbit has grown to infinity and it has become a
homoclinic orbit
. After the bifurcation there is no longer a periodic orbit.
Left panel
: For small parameter values, there is a
saddle point
at the origin and a
limit cycle
in the first quadrant.
Middle panel
: As the bifurcation parameter increases, the limit cycle grows until it exactly intersects the saddle point, yielding an orbit of infinite duration.
Right panel
: When the bifurcation parameter increases further, the limit cycle disappears completely.
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Date | 17 May 2006 (original upload date) | ||
Source | Transferred from en.wikipedia to Commons by Ronhjones using CommonsHelper . | ||
Author | Mathmoclaire at English Wikipedia | ||
Other versions |
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Licensing
Mathmoclaire
at the
English-language Wikipedia
, the copyright holder of this work, hereby publishes it under the following license:
|
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers . | |
Attribution: Mathmoclaire at the English-language Wikipedia | ||
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This licensing tag was added to this file as part of the GFDL licensing update . http://creativecommons.org/licenses/by-sa/3.0/ CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 true true |
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License , Version 1.2 or any later version published by the Free Software Foundation ; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License . Subject to disclaimers . http://www.gnu.org/copyleft/fdl.html GFDL GNU Free Documentation License true true |
Original upload log
The original description page was
here
. All following user names refer to en.wikipedia.
- 2006-05-17 22:47 Mathmoclaire 487×165× (2357 bytes) Author: Claire Postlethwaite. Made in xfig.