M. Argentina et al., COLLIDING WAVES IN A MODEL EXCITABLE MEDIUM - PRESERVATION, ANNIHILATION, AND BIFURCATION, Physical review letters, 79(15), 1997, pp. 2803-2806
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.