具有脉冲效应的两食饵一捕食者系统分析

构建并分析了一个在固定时刻脉冲投放捕食者且具有功能性反应的两食饵一捕食者系统,应用脉冲比较定理和微分方程的分析方法,得到了食饵灭绝周期解稳定的条件和系统持续生存的条件,并数值分析了所得的理论结果.     

一类具有常数脉冲投放的三种群捕食系统

考虑了一类两食饵种群具有密度制约和常数脉冲投放的三种群捕食系统,证明了当无捕食者时系统存在一个正周期解,并讨论了这个正周期解的全局渐近稳定性及其条件.     

具有投放率和时滞的非自治扩散捕食-食饵模型的持久性和周期解

研究了一类具有投放率和时滞的具Beddington-DeAngelis类功能反应的非自治扩散捕食-食饵系统.证明了此系统在一定条件下是持久的,得到了系统存在唯一的全局渐近稳定的正周期解的充分条件.     

具功能反应和投放率的非自治的捕食—食饵系统的周期解和持久性

研究一类具功能反应和投放率的非自治的捕食—食饵系统,证明此系统在一定条件下是一致持续生存的,通过构造适当的Lyapunov函数得到系统存在唯一全局渐近稳定正周期解的充分条件.     

生境修复对具有Monod-Haldane功能反应的食饵捕食者系统的影响分析

为研究生境修复对生态系统产生的影响,文章建立了一类在生境破坏情况下,具有Monod-Haldane功能反应,脉冲比例收获和脉冲常数投放的四种群食饵-捕食者模型.利用脉冲比较定理,Floquent理论及微小扰动法研究了系统的动力学性质,并给出系统中两食饵灭绝和种群持续生存的充分条件.最后,通过数值模拟验证了所得结论.结果显示系统存在一定脆弱性和复杂性,随着生境修复比率和捕食者投放比率的变化,系统将出现拟周期,混沌等复杂的动力学现象.环境修复作用对系统影响的复杂性,也体现了生境修复的重要性.     

具功能反应和投放率的非自治捕食-食饵系统的周期解和持久性

研究一类具Beddington-DeAngeli类功能性反应和投放率的Lotka-Volterra非自治的捕食-食饵系统,证明了此系统在一定条件下是一致持续生存的,通过构造适当的Lyapunov函数得到系统存在唯一全局渐进稳定正周期解的充分条件.并举例说明条件的可行性.     

一类具有不育和脉冲投放的捕食模型

建立了一类具有不育控制和脉冲投放的捕食模型.判断了食饵灭绝周期解存在和全局渐近稳定的充分条件,还得到了种群一致持续生存的充分条件.     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

食饵具群体防卫效应和捕食者具阶段结构的脉冲控制捕食系统

本文研究一类捕食者具有阶段结构和食饵具有群体防卫作用的脉冲控制系统,应用Floquet乘子理论和脉冲比较定理,获得食饵(害虫)灭绝周期解局部稳定和系统持续生存的充分条件,并通过数值例子揭示了系统诸如高倍周期振荡,混沌,吸引子突变,倍周期与半周期分支等复杂的动力学现象.讨论脉冲周期,成年食饵的投放量和群体防卫效应系数对系统的重要作用,得出的结论为实际的害虫管理提供了可靠的策略依据.     

Dynamical study of nutrient-phytoplankton model with toxicity: Effect of diffusion and time delay

A harmful algal bloom is one of the significant concerns of marine biodiversity. The control of such algal bloom is required for the conservation of marine ecology. The proposed work discusses a model for interacting nutrient phytoplankton systems with the effect of toxic chemicals released by phytoplankton and time delay in toxin liberation. Our main aim is to provide a great insight into the impact of toxins and time delay on the dynamics of nutrient-phytoplankton. We investigate the stability of system dynamics, and the condition for the existence of Turing instability is obtained. The role of time delay is also investigated for the proposed system. The numerical simulation shows that toxin release rate, the diffusion coefficient of nutrients, and time delay significantly impact system dynamics. We observe that increasing values of toxin release results in the system dynamics show stable and oscillatory behavior without diffusion. The spatial and spatio-temporal patterns show that the higher value of the rate of toxin release lead to periodic and standing waves. Finally, we observe that the time delay in toxin distribution term stabilizes and destabilizes the system dynamics.     

Job Release: Part of a Hierarchical System to Manage Manufacturing Lead Times in Make-to-order Companies

A methodology to manage manufacturing lead times is currently being developed by the authors. The system is specifically designed to address the needs of small- to medium-sized make-to-order companies. It involves a hierarchical production planning system in which integration between the production and marketing functions is facilitated. Considerations of capacity are included at both of the decision levels addressed—the customer enquiry stage and the job release stage. This paper describes the job release stage, showing how it is linked with the higher-level stage by controlling a hierarchy of backlog lengths. At the job release stage the released backlog length for each work centre is maintained between predetermined minimum and maximum levels. It is shown that shop floor throughput times—an important part of manufacturing lead times—can be controlled by controlling released backlog lengths. The releasing mechanism is described and it is argued that there can be many benefits of job release—including reduced shop congestion, lower work-in-progress and lower costs.     

Impulsive control strategy of a pest management SI model with nonlinear incidence rate

In this work, we consider a pest management SI model with impulsive release of infective pests and spraying pesticides. We prove that all solutions of the investigated system are uniformly ultimately bounded and the pest-extinction periodic solution is globally asymptotically stable when some condition is satisfied. We also obtain the permanent condition of the system. It is concluded that the approach of combining impulsive release of infective pests with impulsive spraying pesticides provides reliable tactic basis for the practical pest management.     

Theoretical study of diffusional release of a dispersed solute from cylindrical polymeric matrix: A novel configuration for providing zero-order release profile

In the context of controlled release drug delivery approaches, the systems providing zero-order release kinetics have special advantages. Through employing these systems, drug concentration could be maintained within the therapeutic window over release time; thus maximum effectiveness alongside minimized side effects of the drug are achieved. However, obtaining zero-order drug release is extremely challenging. One of the main obstacles is the fact that implemented devices should be designed to overcome the decreasing mass transfer driving force, especially, in polymeric systems in which diffusion mechanism is dominant. In this study, we developed a new configuration of a polymeric matrix containing dispersed solute which provides sustained zero-order release. A combination of two innovative approaches including separating baffles and a two-layer coating was proposed to be incorporated into the conventional cylindrical polymeric matrix to induce zero-order release behavior. Then, an approximate mathematical model was developed to investigate the performance of the system under different conditions. The simulated results showed the potential of proposed configuration to be used as a carrier for sustained zero-order release.     

Mathematical modeling of drug delivery from cylindrical implantable devices

A mechanistic mathematical model applicable to the controlled dispersed‐drug release from cylindrical device such as implantable drug delivery system was derived. Analytical solutions based on the pseudosteady state approximation are derived taken account an exact external medium volume. The model prediction is accurate when the initial drug load is higher than the drug solubility in the polymer. The results obtained are compared with the analytical solutions available in the literature. The equations are corroborated by comparison with experimental profiles reported in the literature for sink conditions and non sink conditions. The evolution of concentration distribution profiles is compared for different volume of external medium. A reduction in the volume of the external solution leads to an increase in the concentration on the surface of the device, which determines decreases in the release of drug. One criterion for determining whether the volume of external solution should be considered for the prediction of drug release from cylindrical devices is established. This criterion is based on establishing a maximum percentage error allowed in the values of amount of drug released. The usefulness of the model is focused in the design of implant for controlled release of drug into a small volume of external medium of release. Copyright © 2014 John Wiley & Sons, Ltd.     

An iterative algorithm for scheduling UET tasks with due dates and release times

A new polynomial-time iterative algorithm is presented for the scheduling problem with a unit execution time task system, parallel identical processors, precedence constraints, release times, and the criterion of maximum lateness. For the maximum lateness and makespan problems the algorithm allows to achieve the performance guarantees previously known only for the problems without release times.     

Analytics and numerics of drug release tracking

The study of the dependence of fluxes, concentrations and response times, on the characteristic properties of drug delivery polymeric devices, plays an important role in the design of drug release platforms. The aim of this paper is to develop mathematical tools for an in-depth understanding of drug release tracking. The mathematical model presented takes into account the viscoelastic properties of the polymer and the state of the dispersed drug: free or chemically bound to the matrix. For nonlinear chemical bounds the process is described by a nonlinear integro-differential system and the drug release tracking is treated numerically. For linear chemical bounds closed formulas for the fluxes and response times are established in terms of the parameters that characterize the drug and the platform. These formulas provide a set of a priori estimations for the variables of the model. Numerical examples which show the effectiveness of the approach are included.     

卡托普利缓释片释放过程的灰色数学模型

目的:用灰色理论研究卡托普利缓释片的体外释放过程.方法:采用羧甲基纤维素钠为骨架材料制备缓释片,通过体外释放试验,根据灰色数学模型,预测卡托普利缓释片的体外释放过程.结果:预测值与实测值的平均绝对误差E为0.532,平均相对误差为1.059%.结论:为卡托普利缓释片的临床合理化用药提供了理论依据.     

Dynamical analysis of a new microbial pesticide model with the Monod growth rate

In this paper, a new mathematical model for the entomopathogenic nematode with the Monod growth rate is formulated. Firstly, continuous release of the entomopathogenic nematode is considered. The existence of limit cycles, the Hopf bifurcation and the stability of the periodic solution created by the bifurcation are proved. The sufficient conditions for the globally asymptotical stability of system are obtained. Secondly, impulsive release of the entomopathogenic nematode is also considered. By using the Floquet’s theorem and the small amplitude perturbations, we show that the pest-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. Thus, we provide mathematical evidence on how to release the entomopathogenic nematode in order to control pests at acceptably low levels.