#bifurcation
3 concepts
Concepts
Bifurcation
Bifurcation is when qualitative behavior of a dynamical system suddenly changes as a parameter varies. New fixed points may appear or stability may change.
Bifurcation Theory
Studies phenomena where qualitative properties of dynamical systems change abruptly with parameter variation. Includes saddle-node, Hopf bifurcations.
Center Manifold
An invariant manifold tangent to neutral directions (zero eigenvalues) near a fixed point. Essential for bifurcation analysis and dimension reduction.