COLLIDING WAVES IN A MODEL EXCITABLE MEDIUM - PRESERVATION, ANNIHILATION, AND BIFURCATION

We analyze the transition from annihilation to preservation of collidi ng waves. The analysis exploits the similarity between the local and g lobal 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 pa rallels to the nucleation theory of first-order phase transitions.