Search results
Results From The WOW.Com Content Network
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork bifurcations, like Hopf bifurcations , have two types – supercritical and subcritical.
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
A transverse bifurcation of a heteroclinic cycle is caused when the real part of a transverse eigenvalue of one of the equilibria in the cycle passes through zero. This will also cause a change in stability of the heteroclinic cycle. Infinite-period bifurcation in which a stable node and saddle point simultaneously occur on a limit cycle. [5]
Diagram showing pitchfork bifurcation geometry given by a slice through cusp catastrophe. Date: 1 December 2005: Source: Created in OpenOffice Draw, exported as SVG, size explicitly added in text editor. Author: Jheald: SVG development
In the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other. The term 'saddle-node bifurcation' is most often used in reference to continuous dynamical systems.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
A navigational box that can be placed at the bottom of articles. Template parameters [Edit template data] Parameter Description Type Status State state The initial visibility of the navbox Suggested values collapsed expanded autocollapse String suggested Template transclusions Transclusion maintenance Check completeness of transclusions The above documentation is transcluded from Template ...
But when the mass reaches a certain point – the bifurcation point – the beam will suddenly buckle, in a direction dependent on minor imperfections in the setup. This is an example of a pitchfork bifurcation. Changes in the control parameter eventually changed the qualitative behavior of the system.