一个供应链系统的可靠性模型的适定性分析

供应链系统是一个复杂的动态系统,许多影响因素的存在,使得供应链系统具有强烈的随机性,从而直接影响供应链系统的可靠性,我们通过分析供应链系统的状态之间的转移关系,引入增补变量法,用偏微分方程组建立了供应链系统的可靠性模型,并对该模型系统解的存在唯一性进行了讨论和证明.     

基础模糊命题演算系统BL~*的改进系统

基础模糊命题演算系统BL*是一个和基础命题演算系统BL相对独立的命题演算系统。命题演算系统L*是系统BL*的扩张,但不是系统BL的扩张。通过对系统BL*及其它模糊命题演算系统的研究,本文对BL*系统进行了修正,进一步改进了BL*系统中的公理体系。     

加权演化的港口网络模型的研究

港口系统的发展、演化对国民经济的繁荣发展起着至关重要的作用,因此如何定量地描述港口系统的发展、演化规律也就显得尤为关键,由此出发,从整体论的角度把港口系统作为一个整体来进行系统研究,利用复杂网络的特性,提出了一个真实的随时间演化的港口系统发展、演化模型,该模型能够有效地再现实际港口系统的一些统计特性,这些特性对于了解港口系统的运行状态和对于港口容错能力的优化将具有十分重要的意义.     

拓扑系统的紧性和分离性

考察拓扑系统的两种紧性——空间式紧和locale式紧,给出紧性的若干刻画,讨论了两种紧性的相互关系,证明了拓扑系统的两种紧性都是拓扑空间紧性的良好推广,说明了紧拓扑系统的闭子拓扑系统、有限和系统以及积系统仍是紧拓扑系统。最后在拓扑系统中考察了紧性加强分离性的问题,得到了紧,(强)T2拓扑系统为(强)T3,(强)T4拓扑系统等结论,并用理想收敛刻画了拓扑系统的强T2分离性。     

适应镇定了的AR系统的稳定性

由鞅差序列驱动的 ARX系统经适应镇定后导致闭环系统在均方意义稳定 ,但此时系统的稳定性并不清楚 .在噪声满足一定的条件下 ,本文证明了此闭环系统就是稳定的     

非线性控制系统的梯度扩张的能达性

研究了仿射非线性控制系统的梯度扩张系统.利用非线性控制系统的微分几何理论,通过计算梯度扩张系统的输出函数沿着输入向量场和系统向量场的李导数,讨论仿射非线性控制系统的梯度扩张系统的能达性分布,研究了非线性控制系统和它的梯度扩张系统的能达性之间的关系,证明了如果梯度扩张系统是能达的,则原非线性控制系统也是能达的.     

具有早期活化储备的可修复系统的解的稳定性分析

研究了具有早期活化储备的可修复系统的解的性态,通过研究系统算子的谱点的分布和求解系统算子的共轭算子进而得到系统的解的渐进稳定性.     

具有止步和中途退出的两不同服务台的可修排队

研究了等待空间有限的两服务台可修排队系统,其中一个服务台可能故障.到达的顾客可能进入系统也可能不进入系统(止步),进入系统的顾客可能因等待的不耐烦而中途退出.利用马尔可夫过程的方法建立了系统稳态概率满足的方程组,通过分块矩阵推导出了系统稳态概率向量的迭代计算公式,由此得到了系统各项性能指标的计算公式.最后,给出了一些数值结果.     

基于线性控制的分数阶混沌系统的对偶投影同步

分数阶混沌系统的对偶同步是一个新的同步方法.有关分数阶混沌系统对偶投影同步的研究较少.基于分数阶系统的稳定性理论,通过设计线性控制器研究了分数阶混沌系统的对偶投影同步.给出了一个实现分数阶混沌系统对偶投影同步的一般方法,推广了现有对偶同步的研究结果,通过分数阶Van der Pol系统和分数阶Willis系统的数值仿真证实了该方法的有效性.     

不含混沌真子系统的Li-Yorke混沌

研究了一类Li-Yorke混沌系统,该系统没有真子系统是Li-Yorke混沌的,我们称之为混沌极小系统.本文证明混沌极小系统是拓扑传递的,而且该系统每个非空开集都包含一个不可数混乱集.混沌极小系统不一定是极小的,本文构造了一个这样的反例.特别地,我们考察了线段连续自映射,指出该类系统都不是混沌极小的,线段上混沌极小子系统的存在性和该系统有正熵是等价的.     

Non-constant positive steady-states of a diffusive predator-prey system in homogeneous environment

In this paper, we investigate the existence and non-existence of non-constant positive steady-states of a diffusive predator-prey interaction system under homogeneous Neumann boundary condition. In homogeneous environment, we show that the predator-prey model with Leslie-Gower functional response has no non-constant positive solution, but the system with a general functional response may have at least one non-constant positive steady-state under some conditions.     

Patterned solutions of a homogenous diffusive predator-prey system of Holling type-III

Acta Mathematicae Applicatae Sinica, English Series - In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of...     

Global Dynamics of a Diffusive Leslie-Gower Predator-prey Model with Fear Effect

A diffusive Leslie-Gower predator-prey model with fear effect is considered in this paper. For the kinetic system, we show that the unique positive equilibrium is globally asymptotically stable. Moreover, we find that high levels of fear could decrease the population densities of both prey and predator in a long time. For the diffusive model, we obtain the similar results under certain conditions.     

具有时滞和基于比率的两种群捕食者-食饵扩散系统的周期解

本文研究了一类具有时滞和基于比率的两种群捕食者—食饵扩散系统，利用重合度理论建立了这类系统正周期解的存在性判据。     

POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY

In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.     

POSITIVE PERIODIC SOLUTION FOR TWO-SPECIES PREDATOR-PREY DIFFUSION-DELAY MODELS WITH FUNCTIONAL RESPONSE

In this paper, a two-species diffusive predator-prey model with time delay and functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.     

A diffusive competition model with a protection zone

This paper is concerned with a two species diffusive competition model with a protection zone for the weak competitor. Our mathematical results imply that when the protection zone is above a certain critical patch size determined by the birth rate of the weak competitor, the weak species almost always survives, but it cannot survive when the protection zone is below the critical size and its competitor is strong enough. While this is the main feature of the model, the actual dynamical behavior of the reaction-diffusion system is more complicated. The key to reveal the main feature of the system lies in a detailed analysis of the attracting regions of its steady-state solutions. Our mathematical analysis shows that, compared with the predator-prey model discussed in [Yihong Du, Junping Shi, A diffusive predator-prey model with a protect zone, J. Differential Equations 226 (2006) 63-91], the protection zone has some essentially different effects on the fine dynamics of the competition model.     

具有脉冲扰动的比率相关功能性反应捕食者-食饵扩散模型的持续生存和周期解

本文考虑一类具有脉冲扰动的比率相关的捕食者一食饵扩散模型,利用比较原理研究了这类系统的持续生存和灭绝性,通过将脉冲反应扩散方程转化为相应的算子方程,并证明了解在适当空间的紧性,得到了周期解的存在性、唯一性和全局稳定性.最后分析了脉冲效应对系统性态的影响.     

Effect of a protection zone in the diffusive Leslie predator-prey model

In this paper, we consider the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone Ω₀ for the prey is introduced. As in earlier work [Y. Du, J. Shi, A diffusive predator-prey model with a protection zone, J. Differential Equations 229 (2006) 63-91; Y. Du, X. Liang, A diffusive competition model with a protection zone, J. Differential Equations 244 (2008) 61-86] we show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over Ω₀ and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω₀ is above the critical patch size. However, our research here reveals significant difference of the model's behavior from the predator-prey model studied in [Y. Du, J. Shi, A diffusive predator-prey model with a protection zone, J. Differential Equations 229 (2006) 63-91] with the same kind of protection zone. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations.     

Interactions of Turing and Hopf bifurcations in an additional food provided diffusive predator-prey model

Complex spatiotemporal dynamics of a diffusive predator-prey system involving additional food supply to predator and intra-specific competition among predator, are investigated. We establish critical conditions of the occurrence of Turing instability, which are necessary and sufficient. Furthermore, we also establish conditions of the occurrence of codimension-2 Turing-Hopf bifurcation and Turing-Turing bifurcation, by exploring interactions of Turing bifurcations and Hopf bifurcation. For Turing-Hopf bifurcation, by analyzing normal form truncated to order 3 which are derived by applying normal form method, it is shown that under proper conditions, diffusive predator-prey system generates interesting spatial, temporal and spatiotemporal patterns, including a pair of spatially inhomogeneous steady states, a spatially homogeneous periodic solution and a pair of spatially inhomogeneous periodic solutions. And numerical simulations are also shown to support theory analysis. Moreover, it is found that proper intra-specific competition among predator helps generate complex spatiotemporal dynamics. And, proper additional food supply to predator helps control the population fluctuations of predator and prey, while large quantity and high quality of additional food supply will lead to the extinction of prey and make predator change the source of food, which finally destroy the ecosystem. These investigations might help understand complex spatiotemporal dynamics of predator-prey system involving additional food supply to predator and intra-specific competition among predator, and help conserve species in an ecosystem via supplying suitable additional food.