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Numerical study of pattern formation in an extended Gray-Scott model. (English) Zbl 1221.35456
Summary: 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.
MSC:
35R60PDEs with randomness, stochastic PDE
35K40Systems of second-order parabolic equations, general
60G35Signal detection and filtering (stochastic processes)
65M06Finite difference methods (IVP of PDE)
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