The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronizatio...The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identifi-cation is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification vari-ables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatio-temporal chaotic systems with uncertain parameters may be realized quickly after controllers are added.展开更多
In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of posit...In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.展开更多
In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of posit...In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.展开更多
This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conforma...This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.展开更多
This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which he...This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients.High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions.Unlike[33],this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model.Several ways for verifying the quality of the numerical solutions are also proposed,which may be of important use for comparisons.展开更多
基金the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151)the Innovative Team Program of Liaoning Educational Committee
文摘The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identifi-cation is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification vari-ables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatio-temporal chaotic systems with uncertain parameters may be realized quickly after controllers are added.
基金Supported by the National Basic Research Program of China (Grant No. 2003CB214603), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0559), and the National Natural Science Foundation of China (Grant No. 4017205)
文摘In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.
基金This work Was partially supported by the National Natural Science Foundation of China(Grant No.10471022)
文摘In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.
文摘This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.
基金The first and the third authors are partially supported by HKBU FRG grants and the Hong Kong Research Grant CouncilThe second author is partially supported by the Hong Kong RGC grant(No.201710).
文摘This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients.High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions.Unlike[33],this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model.Several ways for verifying the quality of the numerical solutions are also proposed,which may be of important use for comparisons.
