Numerical bifurcation analysis for ODEs

We discuss numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. We further consider the computation of cycles as a boundary value problem, their continuation and bifurcations. Homoclinic orbits can also be computed as (truncated) boundary value problems and numerically continued. On curves of homoclinic orbits further bifurcations can be detected and computed. We discuss the basic numerical methods, the connections between various computational objects, and provide references to the literature and software implementations.