A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be qua...This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.展开更多
This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the differenc...This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.展开更多
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical system...The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.展开更多
The global dynamics of a cholera model with delay is considered. We determine a basic reproduction number R0 which is chosen based on the relative ODE model, and establish that the global dynamics are determined by th...The global dynamics of a cholera model with delay is considered. We determine a basic reproduction number R0 which is chosen based on the relative ODE model, and establish that the global dynamics are determined by the threshold value R0. If R0 〈 1, then the infection-free equilibrium is global asymptotically stable, that is, the cholera dies out; If R0 〉 1, then the unique endemic equilibrium is global asymptotically stable, which means that the infection persists. The results obtained show that the delay does not lead to periodic oscillations. Finally, some numerical simulations support our theoretical results.展开更多
The present paper aims to develop an automatical strategy for generating accurate different-scale microstructures of human tooth enamels(HTEs),and to elaborate a numerical scheme for simulating their elastic responses...The present paper aims to develop an automatical strategy for generating accurate different-scale microstructures of human tooth enamels(HTEs),and to elaborate a numerical scheme for simulating their elastic responses.At first,the strong governing formulation of these microstructures is briefly constructed,and the relevant weak formulation is then deduced based on the virtual work theorem.Afterwards,a subdividing approach,which cuts the elements intercepted by the interfaces between distinct phases automatically,is established with the aid of the level set method(LSM),and the discrete counterpart of the governing formula is obtained by combining the weak formulation derived and a discretized model.To be noted,two silent merits are found when the elaborated strategy is applied:(1) the continents constituting the microstructures of different scales can be arbitrarily-shaped and conveniently reproduced;(2) the periodic boundary condition commonly employed can be enforced on the external surfaces of representative unit cells(RUCs) with no difficulty.Besides,a boundary value problem(BVP) involving a simplified HTE nanostructure is designed,analytically solved,and hereafter applied to verify the correctness of the proposed strategy.It is observed that both the displacement and stress predictions by the computational approach are in good agreement with the relevant analytical results irrespective of the material combinations applied.Eventually,discussions are made on the influence of material organizations of both the 2D and 3D HTE microstructures at the ultrastructural and repeated rod levels,and some concluding remarks are drawn.展开更多
基金Supported by the NNSFC(10071022),Mathematical Tianyuan Foundation of China(Ty10026002-01-05-03)Shanghai Priority Academic Discipline.
文摘A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
基金supported by National Basic Research Program of China (Grant No. 2013CB834100)National Natural Science Foundation of China (Grant Nos. 11571065,11171132 and 11201173)
文摘This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.
基金supported by National Natural Science Foundation of China(Grant Nos.11171026 and 11271175)National Natural Science Foundation of Shandong Province(Grant No.ZR2012AQ026)
文摘This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.
基金National Natural Science Foundation of China(No.19731003,No.19961003)Yunnan Provincial Natural Science Foundation of China(No.1999A0018M,No.2000A0002M)
文摘The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
文摘The global dynamics of a cholera model with delay is considered. We determine a basic reproduction number R0 which is chosen based on the relative ODE model, and establish that the global dynamics are determined by the threshold value R0. If R0 〈 1, then the infection-free equilibrium is global asymptotically stable, that is, the cholera dies out; If R0 〉 1, then the unique endemic equilibrium is global asymptotically stable, which means that the infection persists. The results obtained show that the delay does not lead to periodic oscillations. Finally, some numerical simulations support our theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.51535010,51305362,11372260&11572266)the Fundamental Research Funds for the Central Universities(Grant Nos.2682014BR016&2682016CX024)the China Scholar Council
文摘The present paper aims to develop an automatical strategy for generating accurate different-scale microstructures of human tooth enamels(HTEs),and to elaborate a numerical scheme for simulating their elastic responses.At first,the strong governing formulation of these microstructures is briefly constructed,and the relevant weak formulation is then deduced based on the virtual work theorem.Afterwards,a subdividing approach,which cuts the elements intercepted by the interfaces between distinct phases automatically,is established with the aid of the level set method(LSM),and the discrete counterpart of the governing formula is obtained by combining the weak formulation derived and a discretized model.To be noted,two silent merits are found when the elaborated strategy is applied:(1) the continents constituting the microstructures of different scales can be arbitrarily-shaped and conveniently reproduced;(2) the periodic boundary condition commonly employed can be enforced on the external surfaces of representative unit cells(RUCs) with no difficulty.Besides,a boundary value problem(BVP) involving a simplified HTE nanostructure is designed,analytically solved,and hereafter applied to verify the correctness of the proposed strategy.It is observed that both the displacement and stress predictions by the computational approach are in good agreement with the relevant analytical results irrespective of the material combinations applied.Eventually,discussions are made on the influence of material organizations of both the 2D and 3D HTE microstructures at the ultrastructural and repeated rod levels,and some concluding remarks are drawn.
