This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new meth...This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references.The proofs mainly rely on Leray-Schauder degree theory,implicit function theorem and analytical techniques.展开更多
This paper studies bistable wavefronts of a diffusive time-periodic Lotka-Volterra system.We obtain a new condition for the existence,uniqueness and stability of bistable timeperiodic traveling waves.This condition is...This paper studies bistable wavefronts of a diffusive time-periodic Lotka-Volterra system.We obtain a new condition for the existence,uniqueness and stability of bistable timeperiodic traveling waves.This condition is sharp and greatly improves the result established in the reference(X.Bao and Z.Wang,Journal of Differential Equations,255(2013)2402-2435).An example is given to demonstrate our consequence.展开更多
In this paper, we deal with the model with a very general growth law and an M- driven diffusion For the general case of time dependent functions M and #, the existence and uniqueness for positive solution is obtained....In this paper, we deal with the model with a very general growth law and an M- driven diffusion For the general case of time dependent functions M and #, the existence and uniqueness for positive solution is obtained. If M and # are T0-periodic functions in t, then there is an attractive positive periodic solution. Furthermore, if M and # are time-independent, then the non-constant stationary solution M（x） is globally stable. Thus, we can easily formulate the conditions deriving the above behaviors for specific population models with the logistic growth law, Gilpin-Ayala growth law and Gompertz growth law, respectively. We answer an open problem proposed by L. Korobenko and E. Braverman in [Can. Appl. Math. Quart. 17（2009） 85-104].展开更多
In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for...In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.展开更多
基金supported by the National Natural Science Foundation of China(No.11671359)the Science Foundation of Zhejiang Sci-Tech University under Grant No.15062173-Ysupported by the provincial Natural Science Foundation of Zhejiang(LY16A010009)
文摘This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references.The proofs mainly rely on Leray-Schauder degree theory,implicit function theorem and analytical techniques.
基金Supported by the National Natural Science Foundation of China(12071434,11671359)the NSERC discovery grant(RGPIN2016-04709)。
文摘This paper studies bistable wavefronts of a diffusive time-periodic Lotka-Volterra system.We obtain a new condition for the existence,uniqueness and stability of bistable timeperiodic traveling waves.This condition is sharp and greatly improves the result established in the reference(X.Bao and Z.Wang,Journal of Differential Equations,255(2013)2402-2435).An example is given to demonstrate our consequence.
基金Supported by the National Natural Science Foundation of China(11271342)
文摘In this paper, we deal with the model with a very general growth law and an M- driven diffusion For the general case of time dependent functions M and #, the existence and uniqueness for positive solution is obtained. If M and # are T0-periodic functions in t, then there is an attractive positive periodic solution. Furthermore, if M and # are time-independent, then the non-constant stationary solution M（x） is globally stable. Thus, we can easily formulate the conditions deriving the above behaviors for specific population models with the logistic growth law, Gilpin-Ayala growth law and Gompertz growth law, respectively. We answer an open problem proposed by L. Korobenko and E. Braverman in [Can. Appl. Math. Quart. 17（2009） 85-104].
基金partially supported by the National Natural Science Foundation of China(11671359)the Provincial Natural Science Foundation of Zhejiang(LY15A010017,LY16A010009)the Science Foundation of Zhejiang Sci-Tech University 15062173-Y
文摘In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.
