In this paper, superlattice patterns have been investigated by using a two linearly coupled Brusselator model. It is found that superlattice patterns can only be induced in the sub-system with the short wavelength. Th...In this paper, superlattice patterns have been investigated by using a two linearly coupled Brusselator model. It is found that superlattice patterns can only be induced in the sub-system with the short wavelength. Three different coupling methods have been used in order to investigate the mode interaction between the two Turing modes. It is proved in the simulations that interaction between activators in the two sub-systems leads to spontaneous formation of black eye pattern and/or white eye patterns while interaction between inhibitors leads to spontaneous formation of super-hexagonal pattern. It is also demonstrated that the same symmetries of the two modes and suitable wavelength ratio of the two modes should also be satisfied to form superlattice patterns.展开更多
A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary ...A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.展开更多
The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential condition...The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential conditions for Turing instability are obtained.It indicates that the emergence of cross-diffusion terms leads to the destabilizing mechanism.Then the amplitude equations and the asymptotic solutions of the model closed to the onset of instability are derived by using the weakly nonlinear analysis.展开更多
This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of...This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of the Hopf bifurcation are obtained.When the diffusion term of the system appears,the stable conditions of positive equilibrium and the Turing instability condition are also obtained.Turing instability is induced by the diffusion term through theoretical analysis.Thus,the region of parameters in which Turing instability occurs is presented.Then the amplitude equations are derived by the multiple scale method.The results will enrich the pattern dynamics in predator⁃prey systems.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
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
HONG KONG,Dec.19(Xinhua)--The resources China funnels into college education,along with its vast talent pool,will help foster the development of artificial intelligence(AI),said 1986 Turing Award winner John Edward Ho...HONG KONG,Dec.19(Xinhua)--The resources China funnels into college education,along with its vast talent pool,will help foster the development of artificial intelligence(AI),said 1986 Turing Award winner John Edward Hopcroft on Friday on the sidelines of the inaugural Hong Kong AI Art Festival.展开更多
Achieving industrial-level electrochemical CO_(2)reduction to formate remains a significant challenge due to limitations in catalyst selectivity and interfacial proton management at high current densities.In a recent ...Achieving industrial-level electrochemical CO_(2)reduction to formate remains a significant challenge due to limitations in catalyst selectivity and interfacial proton management at high current densities.In a recent study,Prof.Guo and colleagues report the development of Turingstructured electrocatalysts,which incorporate reaction-diffusion-inspired topologies to engineer mesoscale surface patterns.This design enables precise modulation of the interfacial microenvironment,enhancing CO_(2)activation and suppressing competing hydrogen evolution.The resulting catalysts achieve efficient and stable CO_(2)-to-formate conversion under industrially relevant conditions,offering a promising strategy for scalable carbon-neutral chemical production.展开更多
This paper is concerned with a classical two-species prey-predator reaction-diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangl...This paper is concerned with a classical two-species prey-predator reaction-diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangle domain.By analyzing the associated eigenvalue problem,the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of system at the constant coexistence equilibrium are established.Then when the bifurcation parameter is in the interior of range for Turing instability and near Turing bifurcation curve,the amplitude equations of the original system near the constant coexistence equilibrium are obtained by multiple-scale time perturbation analysis.On the basis of the obtained amplitude equations,the stability and classifications of spatiotemporal patterns of the original system at the constant coexistence equilibrium are discussed.Finally,to verify the validity of the obtained theoretical results,numerical simulations are also carried out.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10975043, 10947166 and 10775037the Foundation of Bureau of Education, Hebei Province, China under Grant No. 2009108the Natural Science Foundation of Hebei Province, China under Grant No. A2008000564)
文摘In this paper, superlattice patterns have been investigated by using a two linearly coupled Brusselator model. It is found that superlattice patterns can only be induced in the sub-system with the short wavelength. Three different coupling methods have been used in order to investigate the mode interaction between the two Turing modes. It is proved in the simulations that interaction between activators in the two sub-systems leads to spontaneous formation of black eye pattern and/or white eye patterns while interaction between inhibitors leads to spontaneous formation of super-hexagonal pattern. It is also demonstrated that the same symmetries of the two modes and suitable wavelength ratio of the two modes should also be satisfied to form superlattice patterns.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275065,12275064,12475203)the Natural Science Foundation of Hebei Province(Grant Nos.A2021201010 and A2024201020)+3 种基金Interdisciplinary Research Program of Natural Science of Hebei University(Grant No.DXK202108)Hebei Provincial Central Government Guiding Local Science and Technology Development Funds(Grant No.236Z1501G)Scientific Research and Innovation Team Foundation of Hebei University(Grant No.IT2023B03)the Excellent Youth Research Innovation Team of Hebei University(Grant No.QNTD202402)。
文摘A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.
基金National Natural Science Foundation of China(No.11371087)
文摘The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential conditions for Turing instability are obtained.It indicates that the emergence of cross-diffusion terms leads to the destabilizing mechanism.Then the amplitude equations and the asymptotic solutions of the model closed to the onset of instability are derived by using the weakly nonlinear analysis.
基金National Natural Science Foundation of China(No.11971143)。
文摘This paper mainly focus on the research of a predator⁃prey system with Gompertz growth of prey.When the system does not contain diffusion,the stability conditions of positive equilibrium and the occurring condition of the Hopf bifurcation are obtained.When the diffusion term of the system appears,the stable conditions of positive equilibrium and the Turing instability condition are also obtained.Turing instability is induced by the diffusion term through theoretical analysis.Thus,the region of parameters in which Turing instability occurs is presented.Then the amplitude equations are derived by the multiple scale method.The results will enrich the pattern dynamics in predator⁃prey systems.
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.
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.
文摘HONG KONG,Dec.19(Xinhua)--The resources China funnels into college education,along with its vast talent pool,will help foster the development of artificial intelligence(AI),said 1986 Turing Award winner John Edward Hopcroft on Friday on the sidelines of the inaugural Hong Kong AI Art Festival.
基金financially supported by the National Natural Science Foundation of China(No.22209024)Tongcheng R&D Foundation(No.CPCIF-RA-0102)the State Key Laboratory of Advanced Fiber Materials,Donghua University
文摘Achieving industrial-level electrochemical CO_(2)reduction to formate remains a significant challenge due to limitations in catalyst selectivity and interfacial proton management at high current densities.In a recent study,Prof.Guo and colleagues report the development of Turingstructured electrocatalysts,which incorporate reaction-diffusion-inspired topologies to engineer mesoscale surface patterns.This design enables precise modulation of the interfacial microenvironment,enhancing CO_(2)activation and suppressing competing hydrogen evolution.The resulting catalysts achieve efficient and stable CO_(2)-to-formate conversion under industrially relevant conditions,offering a promising strategy for scalable carbon-neutral chemical production.
基金supported by the National Natural Science Foundation of China(No.12261054)Natural Science Foundation of Gansu Province of China(No.22JR5RA346).
文摘This paper is concerned with a classical two-species prey-predator reaction-diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangle domain.By analyzing the associated eigenvalue problem,the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of system at the constant coexistence equilibrium are established.Then when the bifurcation parameter is in the interior of range for Turing instability and near Turing bifurcation curve,the amplitude equations of the original system near the constant coexistence equilibrium are obtained by multiple-scale time perturbation analysis.On the basis of the obtained amplitude equations,the stability and classifications of spatiotemporal patterns of the original system at the constant coexistence equilibrium are discussed.Finally,to verify the validity of the obtained theoretical results,numerical simulations are also carried out.
