Moving and jumping spot in a two-dimensional reaction-diffusion model

摘要: We consider a single spot solution for the Schnakenberg model in two-dimensional unit disk singularly perturbed limit of small diffusivity ratio. For large values reaction-time constant, this can undergo two different types instabilities, both due to Hopf bifurcation. The first type induces oscillatory instability height spot. second periodic motion center. use formal asymptotics investigate when these instabilities are triggered, and which one dominates. In parameter regime where occurs, we construct consisting rotating spot, compute its radius rotation angular velocity. Detailed numerical simulations performed validate asymptotic theory, including spots. More complex, non-circular trajectories also explored numerically.