Pulse-splitting for some reaction-diffusion systems in one-space dimension

摘要: Pulse-splitting, or self-replication, behavior is studied for some two-component singularly perturbed reaction-diffusion systems on a one-dimensional spatial domain. For the Gierer-Meinhardt model in weak interaction regime, characterized by asymptotically small activator and inhibitor diffusivities, numerical approach used to verify key bifurcation spectral conditions of Ei et al. [Japan. J. Indust. Appl. Math., 18, (2001)] that are believed be essential occurrence pulse-splitting system. The observed here edge-splitting, where only spikes closest boundary able replicate. Gray-Scott model, it shown numerically there two types depending parameter regime: edge-splitting simultaneous splitting semi-strong regime. spike one solution components localized, we construct several all can verified analytically, yet no observed. These examples suggest an extra condition, referred as multi-bump transition also required behavior. This condition fact satisfied their regimes.