This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:
Systems: Dynamical systems Mid‑importance This article is within the scope of WikiProject Systems, which collaborates on articles related to systems and systems science.SystemsWikipedia:WikiProject SystemsTemplate:WikiProject SystemsSystems Mid This article has been rated as Mid-importance on the project's importance scale. This article is within the field of Dynamical systems.

sample saddle node equation has variables x1, x2. but figure on right has axes labeled x,y. is this an error?

Fixed. Gandalf61 14:06, 6 May 2006 (UTC)[reply]

Hi, I have been reading this page now for a while now and it seems to make no sence. To find the fixed points should you not put x= mew + x²> thus giving the fixed values as

1/2 +/- sqrt(1/4-mew).

Please could someone comment

No, you are confusing discrete maps, x(n+1)=f(x(n)), with continuous differential equations, dx/dt=f(x). For differential equations, fixed points are dx/dt=0, so f(x)=0. A common confusion. Paul Matthews 15:23, 10 October 2007 (UTC)[reply]

Animated figure runs too fast to be observed. Can't it be made little slower. 195.150.224.236 13:30, 16 June 2006 (UTC)[reply]

I agree! Totally! Please make it slower! ... whoever still has the according code. —Preceding unsigned comment added by 88.75.227.55 (talk) 19:02, 28 September 2008 (UTC)[reply]

I absolutely agree. Can someone do something with it? Even removing it would be better. Burivykh (talk) 15:10, 5 June 2009 (UTC)[reply]

Hi, the animation is too fast so that I can't see different phase portrait when alpha is changing...it's worthless. —Preceding unsigned comment added by 136.159.127.42 (talk) 11:25, 26 February 2010 (UTC)[reply]

As far as I know, the "blue skies bifurcation" is not the saddle-node one, but simply an another word for Blue sky catastrophe (see also Scholarpedia). And the latter is very important, exactly as an example of how a cycle can disappear without a s.-n. bifurcation (when it simply passes to the complex domain), really disappearing! Burivykh (talk) 15:10, 5 June 2009 (UTC)[reply]

From Steven H. Strogatz, "Nonlinear Dynamics and Chaos", Addison Wesley publishing company, 1994.,--> "The prize for most inventive terminology must go to the Abraham and Shaw(1988), who write of a blue sky bifurcation. This term comes from viewing a saddle-node bifurcation in the other direction: a pair of fixed point appears "out of the clear blue sky" as a parameter is varied." —Preceding unsigned comment added by 136.159.127.42 (talk) 11:33, 26 February 2010 (UTC)[reply]

MathWorld has Saddle-node bifurcation as a synonym for fold bifurcation, but this is not what is stated in the article. Not that MathWorld should have the final say but unless there is some evidence to support there being a difference then the article should be changed and possibly renamed to match MathWorld terminology.--RDBury (talk) 01:39, 14 February 2010 (UTC)[reply]

Strogatz on p47. also writes

Admittedly the term saddle-node doesn't make much sense for vector fields on the line. The name derives from a completely analogous bifurcation seen in a higher-dimensional context, such as vector fields on the plane, where fixed points known as saddles and nodes can collide and annihilate.

I feel it is worth to mention here that a saddle point in a 1d flow field is not the same as an unstable fixed point. The unstable and stable fixed points in the normal form of the saddle-node bifurcations are technically neither a saddle nor a node (in contrast to the current article text). ~2026-17476-02 (talk) 09:52, 20 March 2026 (UTC)[reply]