The steady states and convergence to equilibria for a 1‐D chemotaxis model with volume‐filling effect

We consider a chemotaxis model with volume‐filling effect introduced by Hillen and Painter. They also proved the existence of global solutions for a compact Riemannian manifold without boundary. Moreover, the existence of a global attractor in W^{1, p}(Ω??ⁿ), p>n, p?2, was proved by Wrzosek. He also proved that the ω‐limit set consists of regular stationary solutions. In this paper, we prove that the 1‐D stationary problem has at most an infinitely countable number of regular solutions. Furthermore, we show that as t→∞ the solution of the 1‐D evolution problem converges to an equilibrium in W^{1, p}, p?2. Copyright © 2009 John Wiley & Sons, Ltd.     

Transitions in a logistic population model incorporating an Allee effect

In some species, the population may decline to zero; that is, the species becomes extinct if the population falls below a given threshold. This phenomenon is well known as an Allee effect. In most Allee models, the model parameters are constants, and the population tends either to a nonzero limiting state (survival) or to zero (extinction). However, when environmental changes occur, these parameters may be slowly varying functions of time. Then, application of multitiming techniques allows us to construct approximations to the evolving population in cases where the population survives to a slowly varying surviving state and those where the population declines to zero. Here, we investigate the solution of a logistic population model exhibiting an Allee effect, when the carrying capacity and the limiting density interchange roles, via a transition point. We combine multiscaling analysis with local asymptotic analysis at the transition point to obtain an overall expression for the evolution of the population. We show that this shows excellent agreement with the results of numerical computations. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiscaling analysis of a slowly varying single species population model displaying an Allee effect

We consider the growth of a single species population modelled by a logistic equation modified to accommodate an Allee effect, in which the model parameters are slowly varying functions of time. We apply a multitiming technique to construct general approximate expressions for the evolving population in the case where the population survives to a (slowly varying) finite positive limiting state, and that where the population declines to extinction. We show that these expressions give excellent agreement with the results of numerical calculations for particular instances of the changing model parameters. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of dimension 4 in Aleksandrov's problem of filling a space by polyhedra

This paper deals with filling the hyperbolic space Hⁿ by non-compact polyhedra. In dimensions n <4 the non-compact case is very different from the compact one, which was investigated by A.D. Aleksandrov. For n 4 the compact and non-compact cases are almost similar. This investigation is closely related to deformations of complete and incomplete hyperbolic orbifolds (in the sense of W. Thurston) for which a strong rigidity result is proved-similar to the one for complete hyperbolic manifolds in dimension exceeding two.     

The effect of impulsive vaccination on an SIR epidemic model

In this paper, an SIR epidemic model is constructed and analyzed. We get the result that if the parameters satisfy the condition β>α+γ+b, then the disease will be ultimately permanent. Under this condition, we consider how the impulsive vaccination affects the original system. The sufficient condition for the global asymptotical stability of the disease-eradication solution is obtained. We also get that if the impulsive vaccination rate is less than some value, the disease will be permanent, and the disease cannot be controlled. People can select appropriate vaccination rate according to our theoretical result to control diseases.     

抗艾滋病药物的评价与预测模型

第一问中对CD4数量和HIV浓度随周期变化分别建立线性模型和二次模型,由数据确立中度患者CD4随时间变化模型为：C（T）=0．0496T＋3．0659,HIV随时间变化为：H（T）=0．0044T^2—0．2317T＋4.2899．确定最佳治疗终止时间为：轻度患者28．90周,中度患者31．97周,重度患者为40．86周,平均最佳终止治疗时间33．91周．第二问中得出疗法4效果最好,疗法3次之,疗法1最差．然后通过建立了回归分析模型,对最优疗法进行预测,得到最佳终止治疗时间为25．53用．第三问在第二问的基础上增加了治疗费用对治疗效果的影响,计算得出：疗法3为最优,疗法1次之,疗法2最差．用疗     

An improved continuum skin and proximity effect model for hexagonally packed wires

This work presents approximate but closed-form expressions for “effective” complex-valued magnetic permeability and electric conductivity that represent the effects of proximity and skin effect losses in wound coil with hexagonally packed wires. Previous work is extended by providing improved accuracy versus finite element results for effective permeability and by providing an expression for effective conductivity, which was previously neglected. These material properties can then be used in 2D/axisymmetric finite element models in which the coil is modeled as a coarsely meshed, homogeneous region (i.e., removing the need for modeling each turn in the coil).     

Dynamics of an intraguild predation food web model with strong Allee effect in the basal prey

Since intraguild predation (IGP) is a ubiquitous and important community module in nature and Allee effect has strong impact on population dynamics, in this paper we propose a three-species IGP food web model consisted of the IG predator, IG prey and basal prey, in which the basal prey follows a logistic growth with strong Allee effect. We investigate the local and global dynamics of the model with emphasis on the impact of strong Allee effect. First, positivity and boundedness of solutions are studied. Then existence and stability of the boundary and interior equilibria are presented and the Hopf bifurcation curve at an interior equilibrium is given. The existence of a Hopf bifurcation curve indicates that if competition between the IG prey and IG predator for the basal resource lies below the curve then the interior equilibrium remains stable, while if it lies above the curve then the interior equilibrium loses its stability. In order to explore the impact of Allee effect, the parameter space is classified into sixteen different regions and, in each region, the number of interior equilibria is determined and the corresponding bifurcation diagrams on the Allee threshold are given. The extinction parameter regions of at least one species and the necessary coexistence parameter regions of all three species are provided. In addition, we explore possible dynamical patterns, i.e., the existence of multiple attractors. By theoretical analysis and numerical simulations, we show that the model can have one (i.e. extinction of all species), two (i.e. bi-stability) or three (i.e. tri-stability) attractors. It is also found by simulations that when there exists a unique stable interior equilibrium, the model may generate multiple attracting periodic orbits and the coexistence of all three species is enhanced as the competition between the IG prey and IG predator for the basal resource is close to the Hopf bifurcation curve from below. Our results indicate that the intraguild predation food web model exhibits rich and complex dynamic behaviors and strong Allee effect in the basal prey increases the extinction risk of not only the basal prey but also the IG prey or/and IG predator.     

Scheduling jobs with a general learning effect model

The paper deals with machine scheduling problems with a general learning effect. By the general learning effect, we mean that the actual processing time of a job is not only a non-increasing function of the total weighted normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence, where the weight is a position-dependent weight. We show that even with the introduction of a general learning effect to job processing times, some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.     

The dynamics of an epidemic model for pest control with impulsive effect

In pest control, there are only a few papers on mathematical models of the dynamics of microbial diseases. In this paper a model concerning biologically-based impulsive control strategy for pest control is formulated and analyzed. The paper shows that there exists a globally stable susceptible pest eradication periodic solution when the impulsive period is less than some critical value. Further, the conditions for the permanence of the system are given. In addition, there exists a unique positive periodic solution via bifurcation theory, which implies both the susceptible pest and the infective pest populations oscillate with a positive amplitude. In this case, the susceptible pest population is infected to the maximum extent while the infective pest population has little effect on the crops. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamic, which implies that this model has more complex dynamics, including period-doubling bifurcation, chaos and strange attractors.     

The average value inequality in sequential effect algebras

A sequential effect algebra （E, 0, 1, ,o） is an effect algebra on which a sequential product o with certain physics properties is defined; in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem： If a, b E （E, 0, 1, , o） and a⊥b and a o b⊥a o b, is it the case that 2（a o b） ≤ a2 b2 ？ In this paper, we construct an example to answer the problem negatively.     

Bullwhip effect in a supply chain model with multiple delivery delays

We develop a model of differential equations for a supply chain with delivery time delays between every adjacent firms. Based on the supply chain model, we provide a new perspective of the bullwhip effect and show that the bullwhip effect is intrinsic in supply chains in the sense that the equilibrium state of each firm in the supply chain is a cumulative forward product of the ratios of order fulfillment and placement between adjacent firms toward the end customer demand. We also show that it is the multiple time delays instead of the constant end consumer demand that determine the stability of the equilibrium states. However, the consumer demand has impacts on the stability of the equilibrium states of the supply chain when the end retailer’s inventory decisions are linearly related to the end consumer demand.     

The effect of replenishment policies on the bullwhip effect: A transfer function approach

An important phenomenon in supply chain management, known as the bullwhip effect, suggests that demand variability increases as one moves up a supply chain. This paper examines the influence of different replenishment policies on the occurrence of the bullwhip effect. The paper demonstrates that certain replenishment policies can in themselves be inducers of the bullwhip effect, while others inherently lower demand variability. The main causes of increase in variability are projections of future demand expectations, which result in over-exaggerated responses to changes in demand. We suggest that through appropriate selection and use of certain replenishment rules, the bullwhip effect can be avoided, subsequently allowing supply chain management costs to be lowered.     

The role of protection zone on species spreading governed by a reaction–diffusion model with strong Allee effect

It is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, in this paper we introduce a protection zone that is governed by a Fisher–KPP nonlinearity, and examine the dynamics of a reaction–diffusion model with strong Allee effect and protection zone. We show the existence of two critical values $0<L_{?}\le L^{?}$, and prove that a vanishing-transition-spreading trichotomy result holds when the length of protection zone is smaller than $L_{?}$; a transition-spreading dichotomy result holds when the length of protection zone is between $L_{?}$ and $L^{?}$; only spreading happens when the length of protection zone is larger than $L^{?}$. This suggests that the protection zone works when its length is larger than the critical value $L_{?}$. Furthermore, we compare two types of protection zone with the same length: a connected one and a separate one, and our results reveal that the former is better for species spreading than the latter.     

Volatility forecasting using stochastic conditional range model with leverage effect

In this paper, we propose a stochastic conditional range model with leverage effect (henceforth SCRL) for volatility forecasting. A maximum likelihood method based on the particle filters is developed to estimate the parameters of the SCRL model. Simulation results show that the proposed methodology performs well. We apply the proposed model and methodology to four stock market indices, the Shanghai Stock Exchange Composite Index of China, the Hang Seng Index of Hong Kong, the Nikkei 225 Index of Japan, and the S&P 500 Index of US. Empirical results highlight the value of incorporating leverage effect into range modeling and forecasting. In particular, the results show that our SCRL model outperforms the conditional autoregressive range model, the conditional autoregressive range model with leverage effect, and the stochastic conditional range model in both in‐sample fit and out‐of‐sample forecast.     

The analytic connectivity in uniform hypergraphs: Properties and computation

The analytic connectivity (AC), defined via solving a series of constrained polynomial optimization problems, serves as a measure of connectivity in hypergraphs. How to compute such a quantity efficiently is important in practice and of theoretical challenge as well due to the non-convex and combinatorial features in its definition. In this article, we first perform a careful analysis of several widely used structured hypergraphs in terms of their properties and heuristic upper bounds of ACs. We then present an affine-scaling method to compute some upper bounds of ACs for uniform hypergraphs. To testify the tightness of the obtained upper bounds, two possible approaches via the Pólya theorem and semidefinite programming respectively are also proposed to verify the lower bounds generated by the obtained upper bounds minus a small gap. Numerical experiments on synthetic datasets are reported to demonstrate the efficiency of our proposed method. Further, we apply our method in hypergraphs constructed from social networks and text analysis to detect the network connectivity and rank the keywords, respectively.     

具有HollingⅡ型功能反应和Allee效应的捕食系统模型

利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性.通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态,探索研究参数的变化对种群大小的影响,阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性.研究结果表明:1)当处理时间处于有效区间内时,处理时间越大种群的稳定共存参数域越大;2)Allee效应的引入使种群的动态行为更为复杂,从而增加了捕食者种群的灭绝风险;3)系统受强Allee效应的影响,种群会出现提前分叉现象,如果继续增加Allee效应就会导致种群灭绝;4)强Allee效应更容易使种群趋向灭绝.所得结论在丰富生态学理论的同时,提出了保护生态学的重要依据.     

The incremental bullwhip effect of operational deviations in an arborescent supply chain with requirements planning

Lee et al. (1997) advocated the idea of sharing demand and order information among different supply chain entities to mitigate the bullwhip effect. Even with full supply chain visibility afforded by IT systems with requirements planning and with no information distortion, we identify a “core” bullwhip effect inherent to any supply chain because of the underlying demand characteristics and replenishment lead times. In addition, we quantify an incremental bullwhip effect as various operational deviations (inaccurate order placements, batching, lag in sharing demand forecast) contribute incrementally to the variance of the order quantity not only at the node where the deviation is taking place but also at all upstream supply chain nodes. We discuss some managerial implications of our results in the context of a UK manufacturer.     

The effect of constant and pulse vaccination on an SIR epidemic model with infectious period

In this paper, we investigate two delayed SIR models with vaccination and a generalized nonlinear incidence and obtain sufficient conditions for eradication and permanence of the disease, respectively. Our results indicate that a larger vaccination rate will lead to the eradication of a disease. Furthermore, theoretical results show that constant vaccination strategy can lead to disease eradication at relatively low values of vaccination than pulse vaccination strategy, which is different from the results in [1]. In addition, numerical simulations indicate that pulse vaccination strategy or a longer infectious period will make a larger fraction of population infected by disease.