One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the living world. In his seminal paper 'The Chemical Basis of Morphogenesis',...One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the living world. In his seminal paper 'The Chemical Basis of Morphogenesis', Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction.展开更多
We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the ...We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel Epstein model Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.展开更多
文摘One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the living world. In his seminal paper 'The Chemical Basis of Morphogenesis', Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction.
基金The project supported by National Natural Science Foundation of China under Grant No. 10374089 and the Knowledge Innovation Program of the Chinese Academy of Sciences under Grant No. KJCX2-SW-W17
文摘We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel Epstein model Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.
