AJSesinando
Bifurcation and Stability of Equilibria in Dynamical Systems
How the number and stability of equilibrium (stationary) solutions of a parameterized dynamical system change as a parameter varies. Covers fixed points as extrema of a potential, linear stability from the sign of the Jacobian/second derivative, the distinction between stable minima and unstable maxima/saddles, and canonical bifurcations (saddle-node, pitchfork) summarized in a bifurcation diagram. Provides the language for saying a small-noise limit recovers as many stationary states as the potential has critical points.