One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equati...One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.展开更多
Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjectur...Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.展开更多
Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.
Traditionally, the optimization algorithm based on physics principles has some shortcomings such as low population diversity and susceptibility to local extrema. A new optimization algorithm based on kinetic-molecular...Traditionally, the optimization algorithm based on physics principles has some shortcomings such as low population diversity and susceptibility to local extrema. A new optimization algorithm based on kinetic-molecular theory(KMTOA) is proposed. In the KMTOA three operators are designed: attraction, repulsion and wave. The attraction operator simulates the molecular attraction, with the molecules moving towards the optimal ones, which makes possible the optimization. The repulsion operator simulates the molecular repulsion, with the molecules diverging from the optimal ones. The wave operator simulates the thermal molecules moving irregularly, which enlarges the searching spaces and increases the population diversity and global searching ability. Experimental results indicate that KMTOA prevails over other algorithms in the robustness, solution quality, population diversity and convergence speed.展开更多
The model with linear memory arise in the case of a generalized Kirchhoff viscoelastic bar, where a bending-moment relation with memory was considered. In this paper, the exponential decay is proved if the memory kern...The model with linear memory arise in the case of a generalized Kirchhoff viscoelastic bar, where a bending-moment relation with memory was considered. In this paper, the exponential decay is proved if the memory kernal satisfies the condition of the exponential decay. Furthermore, we show that the existence of strong global attractor by verifying the condition （C） introduced in [3].展开更多
By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attrac...By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.展开更多
In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned wi...In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.展开更多
We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attrac...We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.展开更多
The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is ...The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.展开更多
In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differentia...In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincare＇s Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that： （1） the pest population can be controlled below some threshold; （2） compared to single measure, it is more efficient to take two measures for reducing the level of the pests.展开更多
A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochasti...A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.展开更多
In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions ...In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.展开更多
文摘One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.
文摘Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.
基金the NNSF of China(107711597)the NNSF of Gansu(3ZS041A25-006)
文摘Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.
基金Project(61174140)supported by the National Natural Science Foundation of ChinaProject(13JJA002)supported by Hunan Provincial Natural Science Foundation,ChinaProject(20110161110035)supported by the Doctoral Fund of Ministry of Education of China
文摘Traditionally, the optimization algorithm based on physics principles has some shortcomings such as low population diversity and susceptibility to local extrema. A new optimization algorithm based on kinetic-molecular theory(KMTOA) is proposed. In the KMTOA three operators are designed: attraction, repulsion and wave. The attraction operator simulates the molecular attraction, with the molecules moving towards the optimal ones, which makes possible the optimization. The repulsion operator simulates the molecular repulsion, with the molecules diverging from the optimal ones. The wave operator simulates the thermal molecules moving irregularly, which enlarges the searching spaces and increases the population diversity and global searching ability. Experimental results indicate that KMTOA prevails over other algorithms in the robustness, solution quality, population diversity and convergence speed.
基金the National Natural Science Foundation of China (10671158)the Mathematical Tianyuan Foundation of China Grant(10626042)the Natural Science Foundation of Gansu Province (3ZS061-A25-016)
文摘The model with linear memory arise in the case of a generalized Kirchhoff viscoelastic bar, where a bending-moment relation with memory was considered. In this paper, the exponential decay is proved if the memory kernal satisfies the condition of the exponential decay. Furthermore, we show that the existence of strong global attractor by verifying the condition （C） introduced in [3].
基金Project supported by the National Natural Science Foundation of China (No. 19971036)the Trans-Century Training Programme Foundation for the Talents by the Ministry of Education of China.
文摘By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.
基金Acknowledgments The authors thank the referees for their reports and many valuable comments and suggestions that greatly improved the presentation of this paper. The work is supported by the National Natural Science Foundation of China （No. 11261017）, the Key Laboratory of Biological Resources Protection and Utilization of Hubei Province （No. PKLHB1323） and the Key Project of Chinese Ministry of Education （No. 212111）.
文摘In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.
基金The research is supported by the National Science Foundation of Henan Province(No. 0611051800).
文摘We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.
文摘The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.
基金Research is supported by the National Natural Science Foundation of China （11271260）, Shanghai Leading Academic Discipline Project （No. XTKX2012）, the Hujiang Foundation of China （B14005） and the Innovation Program of Shanghai Municipal Education Committee （13ZZ116）.
文摘In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincare＇s Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that： （1） the pest population can be controlled below some threshold; （2） compared to single measure, it is more efficient to take two measures for reducing the level of the pests.
基金This work was supported by the National Natural Science Foundation of P. R. China （No. 11171081, 11171056）, the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology （No. HIT.NSRIF.2011094）, and the Scientific Research Foundation of Harbin Institute of Technology at Weihai （No. HIT （WH） ZB201103）.
文摘A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.
文摘In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.
