Colliding waves in a model excitable medium: Preservation, annihilation, and bifurcation

We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homoclinic Andronov bifurcation, and has parallels to the nucleation theory of first-order phase transitions.