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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]
Created Date: 8/30/2012 4:52:52 PM
Download as PDF; Printable version; ... Biological applications of bifurcation theory; ... Period-doubling bifurcation; Pitchfork bifurcation; S.
All systems exhibiting a certain type of bifurcation are locally (around the equilibrium) topologically equivalent to the normal form of the bifurcation. For example, the normal form of a saddle-node bifurcation is = + where is the bifurcation parameter. The transcritical bifurcation
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.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help ... For Bifurcation theory see Category:Bifurcation theory.