Numerical study of pattern formation in an extended Gray–Scott model

We present the temporal evolution of noise-controlled patterns in a spatially extended Gray–Scott model firstly. We show that the model exhibits a transition from stripe-spot growth to isolated spots, and also to spiral replication. Furthermore, we establish an extended Gray–Scott model with time-varying diffusivity, and find that the patterns exhibit transition from stripe-spot growth to stripe-spot or chaos replication. Additional studies reveal that with noise and time-varying diffusivity together, a new time-dependent pattern—a few of stripes oscillate in the “red” region—emerges, which hasn’t been reported before.