Geometric approach to the bifurcation at infinity: a case study (Q6153430)

This paper considered the relationship between the bifurcation at infinity of the stationary solutions for the reaction-diffusion equation and the connecting orbits of the ordinary differential equations. It answers the question of what kind of solutions appear (or disappear) associated with the bifurcation and clarifies the bifurcation structures of the equilibria in the ordinary differential equation. The dynamics through the one-point compactification called the Bendixson compactification is also shown.