具有反馈控制的Schoner模型的渐近性

本文讨论了具有反馈控制的非自治Schoner系统的持续生存性条件以及该系统为周期系统时，存在唯一严格正的全局稳定的周期解的条件。     

非自治具有扩散率的Schoner模型的持续生存性与周期解

本文讨论了非自治Ｓｃｈｏｎｅｒ系统在无扩散及扩散时持续生存的条件,以及该系统为周期系统时存在唯一严格正的全局稳定周期解的条件。     

基于比率的三种群捕食系统的持续生存

研究一类具有时滞和基于比率的三种群捕食系统,证明该系统在一定条件下是持续生存的;给出无时滞情况下非零平均点的稳定性的充分条件。     

一个稀疏效应下的Volterra系统的极限环

应用数学生态学和微分方程定性理论,讨论了一个稀疏效应下的Volterra系统,在给定参数满足一定的条件下,证明了该系统极限环的存在性和唯一性,以及该系统的正平衡点全局渐近稳定。     

食饵种群具有收获（存放）率的第II类功能性反应模型的定性分析

本文研究了非密度制约的捕食与捕食系统中被捕食者（食饵）种群具有常数收获（存放）率的第Ⅱ类功能性反应模型的定性性质：当该系统具有存放率时,证明了该系统在一定的条件下极限环的存在性、不存在性及唯一性;当该系统具有收获率时,证明了该系统若存在正平衡点,则它是全局不稳定性。     

食饵种群具有收获(存放)率的第Ⅱ类功能性反应模型的定性分析

本文研究了非密度制约的捕食与被捕食系统中被捕食者(食饵)种群具有常数收获(存放)率的第Ⅱ类功能性反应模型的定性性质:当该系统具有存放率时,证明了该系统在一定的条件下极限环的存在性、不存在性及唯一性;当该系统具有收获率时,证明了该系统若存在正平衡点,则它是全局不稳定性.     

具Ⅲ类功能反应的非自治捕食系统的持续性和周期解

本文讨论了一类具Holling Ⅲ类功能反应的非自治捕食系统,得到该系统的持续性和存在唯一全局稳定周期解的充分条件。     

具有时滞和反馈控制的Logistic增长模型的正周期解

首次研究同时具有状态依赖时滞和连续时滞的反馈控制Logistic增长模型,利用重合度理论研究其正周期解的存在性问题,得到了该系统周期正解存在的充分性条件,同时通过构造适当地Lyapunov泛函得到保证该系统（在适当限制下）存在全局稳定周期解的充分性条件,得到一些新结果,所得结果推广和改进了相关文献的主要结果。     

具有Holling Ⅳ类功能反应的三维顺环捕食者-食饵模型

考虑具有Holling Ⅳ类功能反应三维顺环捕食者一食饵系统,利用常微分方程比较定理及Liapunov函数方法,得到了该系统持久性的充分条件,并且对于周期系统在一定条件下。系统存在唯一一个全局渐进稳定的周期正解,最后讨论了概周期解现象,得出了概周期正解的唯一存在性和全局渐进稳定性的充分条件。     

具有无限时滞和扩散项的非自治竞争系统的正周期解(英文)

研究了一类具有无限时滞和扩散项的非自治竞争系统,利用重合度的廷拓定理,得到了该系统正周期解存在的充分性条件.     

Coarse-Grain Modeling of Shear-Induced Binding between von Willebrand Factor and Collagen

Von Willebrand factor (VWF) is a large multimeric protein that aids in blood clotting. Near injury sites, hydrodynamic force from increased blood flow elongates VWF, exposing binding sites for platelets and collagen. To investigate VWF binding to collagen that is exposed on injured arterial surfaces, Brownian dynamics simulations are performed with a coarse-grain molecular model. Accounting for hydrodynamic interactions in the presence of a stationary surface, shear flow conditions are modeled. Binding between beads in coarse-grain VWF and collagen sites on the surface is described via reversible ligand-receptor-type bond formation, which is governed via Bell model kinetics. For conditions in which binding is energetically favored, the model predicts a high probability for binding at low shear conditions; this is counter to experimental observations but in agreement with what prior modeling studies have revealed. To address this discrepancy, an additional binding criterion that depends on the conformation of a submonomer feature in the model local to a given VWF binding site is implemented. The modified model predicts shear-induced binding, in very good agreement with experimental observations; this is true even for conditions in which binding is significantly favored energetically. Biological implications of the model modification are discussed in terms of mechanisms of VWF activity.     

Computer simulation of arterial flow with applications to arterial and aortic stenoses

A computer model for simulating pressure and flow propagation in the human arterial system is developed. The model is based on the one-dimensional flow equations and includes nonlinearities arising from geometry and material properties. Fifty-five arterial segments, representing the various major arteries, are combined to form the model of the arterial system. Particular attention is paid to the development of peripheral pressure and flow pulses under normal flow conditions and under conditions of arterial and aortic stenoses. Results show that the presence of severe arterial stenoses significantly affects the nature of the distal pressure and flow pulses. Aortic stenoses also have a profound effect on central and peripheral pressure pulse formation. Comparison with the published experimental data suggests that the model is capable of simulating arterial flow under normal flow conditions as well as conditions of stenotic obstructions in a satisfactory manner.     

Trends and uncertainties in budburst projections of Norway spruce in Northern Europe

Budburst is regulated by temperature conditions, and a warming climate is associated with earlier budburst. A range of phenology models has been developed to assess climate change effects, and they tend to produce different results. This is mainly caused by different model representations of tree physiology processes, selection of observational data for model parameterization, and selection of climate model data to generate future projections. In this study, we applied (i) Bayesian inference to estimate model parameter values to address uncertainties associated with selection of observational data, (ii) selection of climate model data representative of a larger dataset, and (iii) ensembles modeling over multiple initial conditions, model classes, model parameterizations, and boundary conditions to generate future projections and uncertainty estimates. The ensemble projection indicated that the budburst of Norway spruce in northern Europe will on average take place 10.2 ± 3.7 days earlier in 2051–2080 than in 1971–2000, given climate conditions corresponding to RCP 8.5. Three provenances were assessed separately (one early and two late), and the projections indicated that the relationship among provenance will remain also in a warmer climate. Structurally complex models were more likely to fail predicting budburst for some combinations of site and year than simple models. However, they contributed to the overall picture of current understanding of climate impacts on tree phenology by capturing additional aspects of temperature response, for example, chilling. Model parameterizations based on single sites were more likely to result in model failure than parameterizations based on multiple sites, highlighting that the model parameterization is sensitive to initial conditions and may not perform well under other climate conditions, whether the change is due to a shift in space or over time. By addressing a range of uncertainties, this study showed that ensemble modeling provides a more robust impact assessment than would a single phenology model run.     

Periodic and quasi-periodic behavior in resource-dependent age structured population models

To describe the dynamics of a resource-dependent age structured population, a general non-linear Leslie type model is derived. The dependence on the resources is introduced through the death rates of the reproductive age classes. The conditions assumed in the derivation of the model are regularity and plausible limiting behaviors of the functions in the model. It is shown that the model dynamics restricted to its ω-limit sets is a diffeomorphism of a compact set, and the period-1 fixed points of the model are structurally stable. The loss of stability of the non-zero steady state occurs by a discrete Hopf bifurcation. Under general conditions, and after the loss of stability of the structurally stable steady states, the time evolution of population numbers is periodic or quasi-periodic. Numerical analysis with prototype functions has been performed, and the conditions leading to chaotic behavior in time are discussed.     

Persistence and permanence in a metapopulation model with space-limited recruitment

In this paper we analyze a metapopulation model with space-limited recruitment. The model describes the population dynamics of sessile adult and planktonic larvae in a common larval pool. We introduce the basic reproduction number of each species which is the expected number of future larvae reproduced by one larva. We consider the conditions for the persistence of the multi-species and multi-habitats model and the permanence of the single-species model. Subsequently, we consider the conditions for the existence of the non-trivial steady state of the single-species model and its global stability, and the permanence of the two species and two habitats model.     

Dynamics of HIV infection studied with cellular automata and conformon-P systems

Recently a cellular automaton (CA) has been used to model the dynamics of HIV infection, with interesting results. We replicate and further test this model, and we introduce an alternative model based on conformon-P (cP) systems. We find (in common with other recently published comments) that the CA model is very sensitive to initial conditions and produces appropriate qualitative dynamics only for a narrow range of rule probabilities. In contrast, the cP system model is robust to a wide range of conditions and parameters, with more reproducible qualitative agreement to the overall dynamics and to the densities of healthy and infected cells observed in vivo.     

A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency

A mathematical model comprised of 23 reaction-diffusion equations is used to simulate the biochemical changes and transport of various reactants involved in coagulation and fibrinolysis in quiescent plasma. The growth and lysis of a thrombus, as portrayed by the model equations, is governed by boundary conditions that include the surface concentration of TF-VIIa, the generation of XIa by contact activation (in vitro), and the secretion of tPA due to endothelial activation. We apply the model to two clinically relevant hypercoagulable states, caused by deficiency of either antithrombin III or protein C. These predictions are compared with published experimental data which validate the utility of the developed model under the special case of static conditions. The incorporation of varying hemodynamic conditions in to the current fluid static model remains to be performed.     

Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions

We propose a dynamic model of alcoholic fermentation in wine-making conditions. In this model, the speed at which CO(2) is released is related to the effects of the main factors involved in fermentation in wine-making conditions: temperature (which can vary within a predefined range) and nitrogen additions (which must not exceed the maximal authorized level). The resulting model consists of ordinary differential equations including numerous parameters that need to be identified and important interactions between explicative variables. These parameters were identified by uncoupling the effects of variables during specific experiments. The results were validated on another series of experiments in different conditions.     

Calcium dynamics and vasomotion in arteries subject to isometric, isobaric, and isotonic conditions

In vitro, different techniques are used to study the smooth muscle cells’ calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine.     

Modeling Brain Energy Metabolism and Function: A Multiparametric Monitoring Approach

Mathematical modeling of brain function is an important tool needed for a better understanding of experimental results and clinical situations. In the present study, we are constructing and testing a mathematical model capable of simulating changes in brain energy metabolism that develop in real time under various pathophysiological conditions. The model incorporates the following parameters: cerebral blood flow, partial oxygen pressure, mitochondrial NADH redox state, and extracellular potassium. Accordingly, all the model variables are only time dependent (`point-model' approach). Numerical runs demonstrate the ability of the model to mimic pathological conditions, such as complete and partial ischemia, cortical spreading depression under normoxic and partial ischemic conditions. They also show that, when properly tuned, a model of this type permits the monitoring of only one or two crucial variables and the computation of the remaining variables in real time during clinical or experimental procedures.