Generation and Annihilation

On basis of an exemplary simulation campaign the transition from particle conserving interaction to generation and annihilation phenomena is demonstrated. The transition is controlled by the intrinsic velocity of the dissipative solitons, which is adjusted by varying the time scale constant of the driving inhibitor. The formation of bound states is observed for slow dissipative solitons. With increasing propagator mode amplitude, the interaction processes are complemented by generation through self-completion and finally by annihilation through fading. These observations are the starting point for discussing the mechanisms of generation and annihilation phenomena. Concerning annihilation processes the mechanisms of fading and merging are introduced. The generation of dissipative solitons occurs due to the formation of complex intermediate states, the division of dissipative solitons (self-replication), Turing-destabilization of homogeneous systems, destabilization of single dissipative solitons (self-completion), and interaction of two and more dissipative solitons (replication). Finally, the phenomena of self-completion and replication are related to the superposition of oscillating tails which leads to the formation of a critical nucleus.