FU Zheng-Ping1, XU Xin-Hang1, WANG Hong-Li1,2,3, OUYANG Qi 1,2,3
1School of Physics, Peking University, Beijing 1008712Center for Theoretical Biology, Peking University, Beijing 1008713The Beijing--Hongkong--Singapore Joint Center for Nonlinear and Complex Systems (PKU), Peking University, Beijing 100871
Stochastic Simulation of Turing Patterns
FU Zheng-Ping1;XU Xin-Hang1;WANG Hong-Li1,2,3;OUYANG Qi 1,2,3
1School of Physics, Peking University, Beijing 1008712Center for Theoretical Biology, Peking University, Beijing 1008713The Beijing--Hongkong--Singapore Joint Center for Nonlinear and Complex Systems (PKU), Peking University, Beijing 100871
摘要We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction--diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie's algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion processes are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Stochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.
Abstract：We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction--diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie's algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion processes are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Stochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.
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2008, Vol. 25 
