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A pitchfork bifurcation is a type of local bifurcation where a system transitions from one fixed point to three fixed points. Learn about the supercritical and subcritical cases, the normal forms, and the formal definition of pitchfork bifurcations.
May 24, 2024 · We now consider four classic bifurcations of one-dimensional nonlinear differential equations: saddle-node bifurcation, transcritical bifurcation, supercritical pitchfork bifurcation, and subcritical pitchfork bifurcation.
Learn about different types of bifurcations in two dimensions, including saddle-node, transcritical, pitchfork, and Hopf bifurcations. See examples, prototypes, and phase portraits for each bifurcation.
Learn about bifurcations, qualitative changes in the dynamics of one-dimensional systems as parameters are varied. See examples of saddle-node and pitchfork bifurcations, and how they apply to the budworm population model.
Learn how a pitchfork bifurcation occurs when a system with reflection symmetry has a parameter that changes sign. See how symmetry breaking determines the outcome of the bifurcation and the time evolution of the system.
Oct 10, 2024 · A pitchfork bifurcation is a type of bifurcation in dynamical systems where a single stable fixed point splits into three fixed points, two stable and one unstable. Learn the conditions, the equation and the reference for this bifurcation from Wolfram MathWorld.
A pitchfork bifurcation is a local bifurcation in systems with symmetry. It can be supercritical or subcritical depending on the sign of the third derivative of the bifurcation function.
