Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated ...Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.展开更多
We investigate a reaction-diffusion model in which a Turing pattern develops and reproduces the formation of periodic segments behind a propagating chemical wave front. The chemical scheme involves two species known a...We investigate a reaction-diffusion model in which a Turing pattern develops and reproduces the formation of periodic segments behind a propagating chemical wave front. The chemical scheme involves two species known as activator and inhibitor. The model can be used to mimic the formation of prevertebrae during the early development of vertebrate embryo. Deterministic and stochastic analyses of the reaction-diffusion processes are performed for two typical sets of parameter values, far from and close to the Turing bifurcation. The effects of a local source or sink of inhibitor on the growing structure are studied and successfully compared with experiments performed on chick embryos.We show that fluctuations may lead to the formation of additional prevertebra.展开更多
The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence t...The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence the spatiotemporal property,even the stable dynamic of the system.The local distributed coupling can spatially orient the pattern at an appropriate coupling strength.展开更多
文摘Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.
基金financial support by the international program of scientific cooperation(PICS)of the French national center for scientific research(CNRS)The work was realized within the International Ph.D.Projects Program cofinanced by the Foundation for Polish Science+1 种基金the European Regional Development Fund within the Innovative Economy Operational Program "Grants for Innovation"AL is grateful to the Kavli Institute for Theoretical Physics China(KITPC)for support
文摘We investigate a reaction-diffusion model in which a Turing pattern develops and reproduces the formation of periodic segments behind a propagating chemical wave front. The chemical scheme involves two species known as activator and inhibitor. The model can be used to mimic the formation of prevertebrae during the early development of vertebrate embryo. Deterministic and stochastic analyses of the reaction-diffusion processes are performed for two typical sets of parameter values, far from and close to the Turing bifurcation. The effects of a local source or sink of inhibitor on the growing structure are studied and successfully compared with experiments performed on chick embryos.We show that fluctuations may lead to the formation of additional prevertebra.
文摘The influence of distributed delay coupling on Turing pattern in reaction diffusion system was investigated. Numerical-simulation results proved that the distributed delay of the coupling can significantly influence the spatiotemporal property,even the stable dynamic of the system.The local distributed coupling can spatially orient the pattern at an appropriate coupling strength.
