Qualitative Analysis for Rheodynamic Model of Cardiac Pressure Pulsations

In this paper, we give a rigorous mathematical and complete parameter analysis for the rheodynamic model of cardiac and obtain the conditions and parameter region for global existence and uniqueness of limit cycle and the global bifurcation diagram of limit cycles. We also discuss the resonance phenomenons of the perturbed system.     

军需物资调集规划问题的研究

以军需物资调集为背景 ,在系统分析的基础上建立了全局优化问题的数学规划模型 ,并对模型求解进行了研究 ,提出两阶段规划算法 .仿真计算结果表明所建模型的有效性     

一类三次捕食者-食饵交错扩散系统解的整体存在性和稳定性

首先引进一类三次捕食者-食饵交错扩散系统,该系统是两种群Lotka-Volterra交错扩散系统的推广,现有的已知结果目前很少.本文应用能量估计方法,结合Shauder理论和bootstrap技巧讨论该系统古典整体解的存在唯一性,并在反应函数的系数满足一定条件时,通过构造Lyapunov函数证明系统正平衡点的全局渐近性.     

ANALYSES FOR A MATHEMATICAL MODEL OF THE PATTERN FORMATION ON SHELLS OF MOLLUSCS

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Global existence for a mathematical model of the immune response to cancer

In this paper we study a mathematical model describing the growth of a solid in the presence of an immune system response. The model is strongly coupled degenerate reaction–diffusion system, in which the equations involve discontinuous terms. By using the approximation method combined with energy estimates and the bootstrap arguments, we prove that this system has a global classical solution.     

Existence of global solutions of a macroscopic model of cellular motion in a chemotactic field

Existence of global classical solutions of a class of reaction–diffusion systems with chemotactic terms is demonstrated. This class contains a system of equations derived recently as a continuous limit of the stochastic discrete cellular Potts model. This provides mathematical justification for using numerical solutions of this system for modeling cellular motion in a chemotactic field.     

Global Dynamics of the Oregonator System

In this work, the existence and properties of a global attractor for the solution semiflow of the Oregonator system are proved. The Oregonator system is the mathematical model of the celebrated Belousov–Zhabotinskii reaction. A rescaling and grouping estimation method is developed to show the absorbing property and the asymptotic compactness of the solution trajectories of this three‐component reaction–diffusion system with quadratic nonlinearity. It is also proved that the fractal dimension of the global attractor is finite and an exponential attractor exists for the Oregonator semiflow. Copyright © 2012 John Wiley & Sons, Ltd.     

On the stability of hematopoietic model with feedback control

We propose and analyze a mathematical model of the production and regulation of blood cell population in the bone marrow (hematopoiesis). This model includes the primitive hematopoietic stem cells (PHSC), the three lineages of their progenitors and the corresponding mature blood cells (red blood cells, white cells and platelets). The resulting mathematical model is a nonlinear system of differential equations with several delays corresponding to the cell cycle durations for each type of cells. We investigate the local asymptotic stability of the trivial steady state by analyzing the roots of the characteristic equation. We also prove by a Lyapunov function the global asymptotic stability of this steady state. This situation illustrates the extinction of the cell population in some pathological cases.     

纳入政策预期的国际气候博弈

本研究首先对Baumol和Oates构建的公共外部性模型的假设条件进行修正,从而构建起更符合实际的国际气候治理的数理模型;求解该数理模型,本研究推导出同时实现全球帕累托最优和自身财政收支平衡下,国际环境协议必须遵循的唯一政策规则;最后,以此为基础,本研究进一步构建起纳入政策预期的国际气候博弈模型,并通过数理分析论证,揭示了:如果世界各国都只考虑自身利益最大化,纳入政策预期下的气候博弈的均衡结果,将无法实现全球气候治理的帕累托最优。     

Mathematical Analysis and Pattern Formation for a Partial Immune System Modeling the Spread of an Epidemic Disease

Our motivation is a mathematical model describing the spatial propagation of an epidemic disease through a population. In this model, the pathogen diversity is structured into two clusters and then the population is divided into eight classes which permits to distinguish between the infected/uninfected population with respect to clusters. In this paper, we prove the weak and the global existence results of the solutions for the considered reaction-diffusion system with Neumann boundary. Next, mathematical Turing formulation and numerical simulations are introduced to show the pattern formation for such systems.     

Homogenization results for a coupled system modelling immiscible compressible two-phase flow in porous media by the concept of global pressure

A model for immiscible compressible two-phase flow in heterogeneous porous media is considered. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation) equation with rapidly oscillating porosity function and absolute permeability tensor. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of two-scale convergence.     

Mathematical Analysis of a Chemotaxis-Type Model of Soil Carbon Dynamic

The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a chemotactic term, with the aim to account for the formation of soil aggregations in the bacterial and microorganism spatial organization (hot spot in soil). This is a spatial and chemotactic version of MOMOS (Modelling Organic changes by Micro-Organisms of Soil), a model recently introduced by M. Pansu and his group. The authors present here two forms of chemotactic terms, first a “classical” one and second a function which prevents the overcrowding of microorganisms. They prove in each case the existence of a nonnegative global solution, and investigate its uniqueness and the existence of a global attractor for all the solutions.     

On the global asymptotic stability of the equilibrium of the Lotka-Volterra equations in a varying environment

We consider a mathematical model describing the evolution of prey and predator populations in a varying environment. The model is a system of ordinary differential equations with a unique nontrivial equilibrium. We derive sufficient conditions for the global asymptotic stability of the equilibrium.     

Permanence,extinction and periodic solutions in a mathematical model of cell populations affected by periodic radiation

A periodic mathematical model of cell populations affected by periodic radiation is presented and studied in this paper. We obtain some sufficient conditions on the permanence and extinction of the system. Furthermore, criteria on the existence and global asymptotic stability of unique positive periodic solutions are established. Some numerical examples are shown to verify our results. A discussion is presented for further study.     

On the global optimal solution to an integrated inventory system with general time varying demand,production and deterioration rates

In this paper a unified inventory model for integrated production system with a single product is presented. The production, demand and deterioration rates for the finished product and the deterioration rates for raw materials are assumed to be functions of time. A rigorous mathematical proof which shows the global optimality of the solution to the considered inventory system is introduced. A numerical example that illustrates the solution procedure is included.     

On the dynamical behavior of three species food web model

In this paper, a mathematical model consisting of two preys one predator with Beddington–DeAngelis functional response is proposed and analyzed. The local stability analysis of the system is carried out. The necessary and sufficient conditions for the persistence of three species food web model are obtained. For the biologically reasonable range of parameter values, the global dynamics of the system has been investigated numerically. Number of bifurcation diagrams has been obtained; Lyapunov exponents have been computed for different attractor sets. It is observed that the model has different types of attractors including chaos.     

Existence of global attractors for the coupled system of suspension bridge equations

A mathematical model of the suspension bridge describes the vibration of the road bed in the vertical plain and that of the main cable. We show the existence of an absorbing set for the solution of the problem. Furthermore, the global attractors of the coupled system of suspension bridge are studied by a new semigroup approach.     

Deterministic and stochastic stability of a mathematical model of smoking

Our aim in this paper, is first constructing a Lyapunov function to prove the global stability of the unique smoking-present equilibrium state of a mathematical model of smoking. Next we incorporate random noise into the deterministic model. We show that the stochastic model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. Then a stochastic Lyapunov method is performed to obtain the sufficient conditions for mean square and asymptotic stability in probability of the stochastic model. Our analysis reveals that the stochastic stability of the smoking-present equilibrium state, depends on the magnitude of the intensities of noise as well as the parameters involved within the model system.     

Real-time nonlinear global state observer design for solar heating systems

Nowadays it is important to investigate and develop solar water heating systems as an environmentally friendly technology. For this reason we introduce a physically-based nonlinear mathematical model that applies to a wide range of solar heating systems. In commercial solar heating systems not all state variables are monitored by direct measurements, since some of them may be technically difficult or expensive to measure. For a better monitoring and more efficient control of the system it may be useful to estimate the unmeasured state variables.As a novelty, we apply a global nonlinear state observer to a solar domestic water heating system. The state observer has been established relatively recently in the field of control theory. The state observer we worked out enables us to estimate the unmeasured state variables in real-time. This observer is global in the sense that it works starting from any initial state. A further contribution of this work is a rather general algorithm for the practical application of the real-time estimation process, and we also give bounds of the estimation error and a practical method to decrease this error.Comparing calculated and measured values for a real particular solar heating system, we justify the usability of the state observer and the estimation process.On the basis of measured data, we show that the nonlinear mathematical model corresponding to the applied nonlinear observer is more accurate than the linear model corresponding to the classical linear Luenberger-type observer, so it is reasonable to apply the nonlinear observer.     

A Lyapunov function for the chemostat with variable yields

In this Note, we give a global asymptotic stability result for the competition mathematical model between several species in a chemostat, by using a new Lyapunov function. The model includes both monotone and non-monotone response functions, distinct removal rates for the species and variable yields, depending on the concentration of substrate. We obtain, as corollaries of our result, three global stability theorems which were considered in the literature.