This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dim...This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dimension of the global attractor.展开更多
In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate ass...In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate assumptions, we acquire a precise estimate of the upper bound for its Hausdorff and Fractal dimensions.展开更多
In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source:■where k1 epu≤D（u） or k1 up≤D（u）;k2 equ≤S（u）≤k3 equ;g（u）≤a-...In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source:■where k1 epu≤D（u） or k1 up≤D（u）;k2 equ≤S（u）≤k3 equ;g（u）≤a-beku.It is proved that,if q <k-1 or q=k-1 and b> b0 for some constant b0> 0,then there exists a unique classical solution which is globally bounded.The results show the effect of the aggregation and the logistic damping source on the existence of globally bounded solutions.展开更多
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differen...The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.展开更多
Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and ex...Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.展开更多
In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the...In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the展开更多
In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimension...In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.展开更多
The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for...The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.展开更多
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically esta...In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.展开更多
The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the probl...The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.展开更多
Many rivers originate in high mountainous regions. However, the effects of climate warming on the runoff and water balance in these regions remain unclear due to the lack of observational data from harsh environments,...Many rivers originate in high mountainous regions. However, the effects of climate warming on the runoff and water balance in these regions remain unclear due to the lack of observational data from harsh environments, and the variable influences of climate change on alpine land-cover types with different water balances. Using observations and simulations from Coup Model, water-balance values collected at five alpine land-cover types(steppe, shrub meadow, moist meadow, swamp meadow, and moraine) in a small alpine watershed, the Qilian Mountains in Northwest China, from October 2008 to September 2014, were compared. Measured evapotranspiration, multilayer soil temperatures and water contents, and frozen-depth data were used to validate Coup Model outputs. The results show that elevation is the primary influence on precipitation, evapotranspiration, and runoff coefficients in alpine regions. Land-cover types at higher elevations receive more precipitation and have a larger runoff coefficient. Notably, climate warming not only increases evapotranspiration but also particularly increases the evapotranspiration/precipitation ratio due to an upward shift in the optimum elevation of plant species. These factors lead to decrease runoff coefficients in alpine basins.展开更多
Seismic static stress triggering model is tested using Harvard centroid moment tensor (CMT) solution catalogue of 1976~2000 and concept of earthquake doublet. Result shows that seismic static stress triggering effect ...Seismic static stress triggering model is tested using Harvard centroid moment tensor (CMT) solution catalogue of 1976~2000 and concept of earthquake doublet. Result shows that seismic static stress triggering effect does exist in the view of global earthquakes, but the effect is very weak. Dividing the earthquakes into thrust focal mechanism, normal focal mechanism, strike-slip focal mechanism, we find that non-strike-slip focal mechanism earthquakes have significant triggering effect, whereas, the triggering effect in strike-slip focal mechanism earthquakes is not obvious. Divided the subsequent events delay time of earthquake doublet into 5 classes of t1, t<1, t10, t<10, 1t10 (t is in unit of d), then seismic static stress triggering effect does not change with delay time in short time period after earthquakes. The research on seismic static stress triggering in different regions of the world indicates that triggering effect is significant in subduction belts. Seismic static stress triggering model is tested by using earthquake doublets in China and its adjacent region. The result indicates that seismic static stress triggering effect cannot be observed easily in China and its adjacent region due to the seismic focal mechanism type (most of the earthquakes are strike-slip earthquakes).展开更多
The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9],...The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by DanchinDesjardins [11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms,we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.展开更多
In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of lim...In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.展开更多
The economy is globalizing. But how are the different economic world regions performing regarding globalization of trade flows? Why are they performing differently? Globalization is not only the increase of internatio...The economy is globalizing. But how are the different economic world regions performing regarding globalization of trade flows? Why are they performing differently? Globalization is not only the increase of international trade between certain preferential geographic areas of economy, but also the resulting increase of interweavement of trade flows between different geographical areas, independent of the amount of trade. This paper is a revised and expanded version of the paper entitled “World Trade and Associated Systems Risk of Global Inequality: Empiric Study of Globalization Evolution between 2003-2011 and Regional Pattern Analysis” presented at International Conference on Applied Economics (ICOAE2013), Istanbul, 27-29 June, 2013. This paper analyzes the evolution of world trade flows between 2003-2012 and performs a cross-section analysis of the year 2012. The economic interweavement will be measured by an inequality risk metric applied to the supply-demand matrix. This risk indicator is based on the concept of statistical entropy resulting in an inequality risk measure, giving an indication for the degree of economic globalization and the evolution of globalization in different geographical regions. In addition, it analyses the governing rational of globalization evolution. The result of this research shows that economic trade flows are globalizing, but with clear different regional patterns, not only between globalizing and de-globalizing regions, but also within the globalizing and de-globalizing regions itself. The emerging economies such as China or the Middle East are globalizing whereas mature economies such as North America and Europe are de-globalizing, confirming for globalization of the inverse Kuznets evolution. The different patterns between the different economic world regions can be explained by using the Globalization Type’s Model as well as the Central Theorem of Globalization.展开更多
文摘This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dimension of the global attractor.
文摘In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate assumptions, we acquire a precise estimate of the upper bound for its Hausdorff and Fractal dimensions.
基金supported by Shandong Provincial Natural Science Foundation,China(ZR2017LA003)
文摘In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source:■where k1 epu≤D（u） or k1 up≤D（u）;k2 equ≤S（u）≤k3 equ;g（u）≤a-beku.It is proved that,if q <k-1 or q=k-1 and b> b0 for some constant b0> 0,then there exists a unique classical solution which is globally bounded.The results show the effect of the aggregation and the logistic damping source on the existence of globally bounded solutions.
基金Project supported by the National Natural Science Foundation of China (No.10571078)the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)
文摘The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.
文摘Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.
文摘In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the
文摘In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.
文摘The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
文摘In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.
文摘The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.
基金financial support from the National Natural Sciences Foundation of China(41401041)and the National Basic Research Program of China(2013CBA01806)
文摘Many rivers originate in high mountainous regions. However, the effects of climate warming on the runoff and water balance in these regions remain unclear due to the lack of observational data from harsh environments, and the variable influences of climate change on alpine land-cover types with different water balances. Using observations and simulations from Coup Model, water-balance values collected at five alpine land-cover types(steppe, shrub meadow, moist meadow, swamp meadow, and moraine) in a small alpine watershed, the Qilian Mountains in Northwest China, from October 2008 to September 2014, were compared. Measured evapotranspiration, multilayer soil temperatures and water contents, and frozen-depth data were used to validate Coup Model outputs. The results show that elevation is the primary influence on precipitation, evapotranspiration, and runoff coefficients in alpine regions. Land-cover types at higher elevations receive more precipitation and have a larger runoff coefficient. Notably, climate warming not only increases evapotranspiration but also particularly increases the evapotranspiration/precipitation ratio due to an upward shift in the optimum elevation of plant species. These factors lead to decrease runoff coefficients in alpine basins.
基金Joint Seismological Science Foundation of China (602005).
文摘Seismic static stress triggering model is tested using Harvard centroid moment tensor (CMT) solution catalogue of 1976~2000 and concept of earthquake doublet. Result shows that seismic static stress triggering effect does exist in the view of global earthquakes, but the effect is very weak. Dividing the earthquakes into thrust focal mechanism, normal focal mechanism, strike-slip focal mechanism, we find that non-strike-slip focal mechanism earthquakes have significant triggering effect, whereas, the triggering effect in strike-slip focal mechanism earthquakes is not obvious. Divided the subsequent events delay time of earthquake doublet into 5 classes of t1, t<1, t10, t<10, 1t10 (t is in unit of d), then seismic static stress triggering effect does not change with delay time in short time period after earthquakes. The research on seismic static stress triggering in different regions of the world indicates that triggering effect is significant in subduction belts. Seismic static stress triggering model is tested by using earthquake doublets in China and its adjacent region. The result indicates that seismic static stress triggering effect cannot be observed easily in China and its adjacent region due to the seismic focal mechanism type (most of the earthquakes are strike-slip earthquakes).
基金supported by Natural Science Foundation of Fujian Province(JZ160406)partly supported by National Natural Science Foundation of China-NSAF(11271305 and 11531010)
文摘The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by DanchinDesjardins [11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms,we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.
文摘In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.
文摘The economy is globalizing. But how are the different economic world regions performing regarding globalization of trade flows? Why are they performing differently? Globalization is not only the increase of international trade between certain preferential geographic areas of economy, but also the resulting increase of interweavement of trade flows between different geographical areas, independent of the amount of trade. This paper is a revised and expanded version of the paper entitled “World Trade and Associated Systems Risk of Global Inequality: Empiric Study of Globalization Evolution between 2003-2011 and Regional Pattern Analysis” presented at International Conference on Applied Economics (ICOAE2013), Istanbul, 27-29 June, 2013. This paper analyzes the evolution of world trade flows between 2003-2012 and performs a cross-section analysis of the year 2012. The economic interweavement will be measured by an inequality risk metric applied to the supply-demand matrix. This risk indicator is based on the concept of statistical entropy resulting in an inequality risk measure, giving an indication for the degree of economic globalization and the evolution of globalization in different geographical regions. In addition, it analyses the governing rational of globalization evolution. The result of this research shows that economic trade flows are globalizing, but with clear different regional patterns, not only between globalizing and de-globalizing regions, but also within the globalizing and de-globalizing regions itself. The emerging economies such as China or the Middle East are globalizing whereas mature economies such as North America and Europe are de-globalizing, confirming for globalization of the inverse Kuznets evolution. The different patterns between the different economic world regions can be explained by using the Globalization Type’s Model as well as the Central Theorem of Globalization.
