具有连续时滞和功能性反应的非自治竞争系统的持续生存

本文利用Lyapunov-Razumikhin理论讨论了具有连续时滞和Ⅱ类功能性反应的非自治扩散竞争系统．此系统有两个种群n个斑块，其中一个种群可以在n个斑块中自由扩散，另一种群被限定在一斑块中不能扩散．当系数满足一定的条件时，证明了系统是持续生存的，此外，给出了该系统的一周期解全局吸引的充分条件．     

捕食者和食饵均带有扩散的随机捕食-食饵模型动力学分析

考虑了斑块环境下捕食者种群和食饵种群分别在n个斑块扩散的随机捕食 食饵模型.利用Lyapunov函数法证明了对任意给定的初始值,随机系统全局正解的存在唯一性,并对其进行了有界性分析.此外给出了食饵种群及整个系统灭绝的充分条件.最后通过数值模拟验证了所得理论的正确性.     

脆弱斑块中植物种子的脉冲扩散

考虑了一类脆弱斑块中植物种子的脉冲漂移模型,得到了系统永久持续生存性.在此基础上,利用单调凸算子理论,得到了系统唯一全局渐进稳定的周期解.数值模拟也表明脉冲扩散能挽救脆弱斑块中的植物种群.     

非自治竞争Lotka—Volterra系统的持续生存和全局稳定

本文研究一般ｎ个种群竞争的非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ系统,得到了系统一致持续生存和全局渐近稳定的新的判别准则,这些准则推广了现有有关文献中的一些结果。     

具有扩散的n斑块生态系统的渐近周期解

研究了具有渐近周期系数的两种群扩散竞争系统,该系统由n个斑块组成,其中一种群可以在n个斑块之间扩散,而另一种群在一个斑块中,不能扩散.结合运用Liapunov函数,得到该系统唯一存在全局渐近稳定的渐近周期解的条件.     

非局部时滞Schoner竞争反应扩散方程的行波解

构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型．每一个种群的成熟期是一个常数,而且只有成年种群存在竞争,幼年的种群并不存在竞争,此外种群个体在空间区域中的运动是随机行走的．我们利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论,证明了连接两个边界平衡解的行波解的存在性．     

基于污染环境毒素驱使下扩散的随机单种群系统的生存分析

研究了一类基于污染斑块环境毒素驱使下扩散的单种群模型.通过构造合适的Lyapunov函数分析了系统存在唯一的全局正解,并讨论了解的随机最终有界性;最后获得了种群随机持久、均值持久和灭绝的充分条件.     

分布在非齐次空间中捕食－被捕食系统的锁相振动

本文以经典的带有时滞的捕食－被捕食系统为基础，构造了一类泛函微分方程作为描述分布在由ｎ个岛屿构成的环状区域上的捕食－被捕食种群生长过程的模型．我们假设种群在最相邻的岛屿间相互迁移，以迁移率为分支参数，研究了该系统的锁相振动，给出了离散波分支的存在条件．     

分布在非齐次空间中捕食－被捕食系统的锁相振动

本文以经典的带有时滞的捕食－被捕食系统为基础，构造了一类泛函微分方程作为描述分布在由ｎ个岛屿构成的环状区域上的捕食－被捕食种群生长过程的模型．我们假设种群在最相邻的岛屿间相互迁移，以迁移率为分支参数，研究了该系统的锁相振动，给出了离散波分支的存在条件．     

具有不同扩散率的两种群Ayala竞争模型的持续生存

讨论了具有不同扩散率的两种群Ａｙａｌａ竞争系统之边界平衡点和正平衡点的稳定性,得出了相关种群动力学行为的结论·同时对有扩散和无扩散时种群的动力学行为进行了比较,说明了扩散对种群持续生存的影响·     

DYNAMICS OF A NONLINEAR NON-AUTONOMOUS n-PATCHES PREDATOR-PREY DISPERSION-DELAY MODEL

In this paper,a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied,where all parameters are time-dependent.In this system consisting of n-patches the prey species can disperse among n-patches,but the predator species is confined to one patch and cannot disperse.It is proved that the system is uniformly persistent under any dispersion rate effect.Furthermore,some sufficient conditions are established for the existence of a unique almost periodic solution of the system.The example shows that the criteria in the paper are new,general and easily verifiable.     

一类具有无穷时滞和功能反应的捕食扩散系统的持久性与稳定性

研究一类非自治的具有HollingⅡ类功能性反应且包含时变时滞与多个无穷时滞的两种群n斑块捕食扩散系统的持久性与稳定性.利用比较原理,结合构造Lyapunov泛函的方法,得到了保证该系统永久持续生存和任意正解全局渐近稳定的充分性条件.     

具有扩散和比率依赖的三种群混合模型的分析

本文讨论了捕食者具有比率依赖的功能性反应,食饵与另一种群竞争且自身可以 扩散的混合模型.证明了系统一致持久与扩散有关,而且得到了系统存在全局吸引周期 解的充分条件.     

Permanence of dispersal population model with time delays

Permanence of a dispersal single-species population model is considered where environment is partitioned into several patches and the species requires some time to disperse between the patches. The model is described by delay differential equations. The existence of food-rich patches and small dispersions among the patches are proved to be sufficient to ensure partial permanence of the model. It is also shown that partial permanence ensures permanence if each food-poor patch is connected to at least one food-rich patch and if each pair in food-rich patches is connected. Furthermore, it is proved that partial persistence is ensured even under large dispersion among food-rich patches if the dispersion time is relatively small.     

PERMANENCE OF A NONLINEAR PERIODIC PREDATOR-PREY SYSTEM WITH PREY DISPERSAL AND PREDATOR DENSITY-INDEPENDENCE

In this paper,a set of suffcient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.     

An impulsive periodic predator–prey system with Holling type III functional response and diffusion

This paper studies an impulsive two species periodic predator–prey Lotka–Volterra type dispersal system with Holling type III functional response in a patchy environment, in which the prey species can disperse among n different patches, but the predator species is confined to one patch and cannot disperse. Conditions for the permanence and extinction of the predator–prey system, and for the existence of a unique globally stable periodic solution are established. Numerical examples are shown to verify the validity of our results.     

Permanence and extinction analysis for a delayed periodic predator-prey system with Holling type II response function and diffusion

In this paper, it is studied that two species predator-prey Lotka-Volterra type dispersal system with delay and Holling type II response function, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions of integrable form for the boundedness, permanence, extinction and the existence of positive periodic solution are established, respectively.     

Numerical study of a liquid/liquid slug flow in a micro-reactor

The great advantages of micro–reactors are associated with an extremely high surface–to–volume ratio. Hence, micro–reactors permit promising operating conditions, such as almost perfect heat or mass transfer. The hydrodynamics of a liquid/liquid slug flow in a micro–channel is characterized by complex vortex structures in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persists between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner. To study the physics of this complex liquid/liquid system, a modified level–set method in conjunction with an immersed–boundary formulation is engaged. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of liquid/liquid slug flow in a capillary microreactor

The great advantage of microreactors is associated with an extremely large surface-to-volume ratio. Hence, microreactors permit promising operating conditions, such as almost-perfect heat or mass transfer. This, of course, requires that the hydrodynamics is well understood. The hydrodynamics of a liquid/liquid slug flow in a micro-capillary is characterized by a complex vortex structure in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persist between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner. Apparently, several effects influence the hydrodynamics. The main dimensionless groups are a Reynolds number, a Capillary number, and the ratio of viscosities and densities of both phases. To study the physics of this complex two-liquid system, a modified level-set method in conjunction with an immersed-boundary formulation is engaged. Presently, the simulations are time-dependent and axially-symmetric in nature. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of mass transfer in liquid/liquid slug flow

The mass transport for a liquid/liquid extraction system is examined using a numerical concept following the idea of the interface-tracking method. Separate, body-fitted, static computational domains are arranged around an imported steady-state interface topology. The domains are coupled at the free interface to capture the behaviour of the conjugated system. The steady-state hydrodynamics are the basis for the simulation of the transient mass transport, which is calculated as a passive scalar concentration or one-way coupling. The investigation is restricted to the extraction from the disperse to the continuous phase. Simulation results for an extraction from the disperse to the continuous phase show that most of the mass is transferred through the wall-film region into the continuous phase. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)