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

Weiming Wang; Yezhi Lin; Feng Yang; Lei Zhang; Yongji Tan

doi:10.1016/j.cnsns.2010.09.002

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

Weiming Wang^*, Yezhi Lin, Feng Yang, Lei Zhang, Yongji Tan

^*Corresponding author for this work

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2016-2026
Number of pages	11
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	16
Issue number	4
DOIs	https://doi.org/10.1016/j.cnsns.2010.09.002
State	Published - Apr 2011

Keywords

Gray-Scott model
Noise
Pattern formation
Time-varying diffusivity

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10.1016/j.cnsns.2010.09.002

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title = "Numerical study of pattern formation in an extended Gray-Scott model",

abstract = "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.",

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author = "Weiming Wang and Yezhi Lin and Feng Yang and Lei Zhang and Yongji Tan",

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T1 - Numerical study of pattern formation in an extended Gray-Scott model

AU - Wang, Weiming

AU - Lin, Yezhi

AU - Yang, Feng

AU - Zhang, Lei

AU - Tan, Yongji

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

KW - Gray-Scott model

KW - Noise

KW - Pattern formation

KW - Time-varying diffusivity

UR - https://www.scopus.com/pages/publications/78049362869

U2 - 10.1016/j.cnsns.2010.09.002

DO - 10.1016/j.cnsns.2010.09.002

M3 - 文章

AN - SCOPUS:78049362869

SN - 1007-5704

VL - 16

SP - 2016

EP - 2026

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 4

ER -

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

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Keywords

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