Comments and questions about the
APOD on the main view screen.

neufer
 Vacationer at Tralfamadore
 Posts: 18734
 Joined: Mon Jan 21, 2008 1:57 pm
 Location: Alexandria, Virginia
Post
by neufer » Thu Mar 12, 2020 11:38 am
https://en.wikipedia.org/wiki/Bifurcation_theory wrote:
<<River bifurcation (from Latin: furca, fork) occurs when a river flowing in a single stream separates into two or more separate streams (called distributaries) which continue downstream. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. A local bifurcation occurs when a parameter change causes the stability of an equilibrium (or fixed point) to change. In continuous systems, this corresponds to the real part of an eigenvalue of an equilibrium passing through zero. In discrete systems, this corresponds to a fixed point having a Floquet multiplier with modulus equal to one. In both cases, the equilibrium is nonhyperbolic at the bifurcation point. The topological changes in the phase portrait of the system can be confined to arbitrarily small neighbourhoods of the bifurcating fixed points by moving the bifurcation parameter close to the bifurcation point (hence 'local').>>
Art Neuendorffer

orin stepanek
 Plutopian
 Posts: 7101
 Joined: Wed Jul 27, 2005 3:41 pm
 Location: Nebraska
Post
by orin stepanek » Thu Mar 12, 2020 11:42 am
crs20_boostback1024.jpg
Awsome; that's the way it was done in old movies!
You do not have the required permissions to view the files attached to this post.
Orin
Smile today; tomorrow's another day!

heehaw
Post
by heehaw » Thu Mar 12, 2020 6:53 pm
See you later, bifurcator!