带饱和项的互惠交错扩散模型整体解的存在性和稳定性

应用能量估计方法和Gagliardo-Nirenberg型不等式证明了带饱和项的Shigesada-Kawasaki-Teramoto两种群互惠模型在齐次Neumann边值条件下整体解的存在唯一性和一致有界性.通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的条件.     

分布时滞竞争模型的周期解

研究了分布时滞竞争模型周期解,利用Gaines与Mawhin的重合度理论,通过构造恰当的Lyapunov函数得到模型正周期解的存在性、唯一性及全局稳定性。     

具有庇护所的三种群捕食者-食饵模型

讨论了一类具有庇护所的自治三种群捕食者一食饵模型,运用Liapunov函数方法,得到了该模型持久性的充分条件．对于该模型的周期系统,在一定的条件下,将产生唯一一个全局渐近稳定的周期正解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定性的充分条件．     

一类食饵具有S-型变收获率的非自治离散捕食系统渐近行为

建立并研究了一类具有S-型变收获率的非自治离散捕食系统,应用差分不等式、Brouwer不动点定理和分析技巧分别建立了系统的持久生存性,正周期解的存在性及全局渐近稳定性的充分条件,我们还给出了具体验证例子及相应的数值模拟结果.     

Global dynamics and bifurcation analysis of a host–parasitoid model with strong Allee effect

In this paper, we study the global dynamics and bifurcations of a two-dimensional discrete time host–parasitoid model with strong Allee effect. The existence of fixed points and their stability are analysed in all allowed parametric region. The bifurcation analysis shows that the model can undergo fold bifurcation and Neimark–Sacker bifurcation. As the parameters vary in a small neighbourhood of the Neimark–Sacker bifurcation condition, the unique positive fixed point changes its stability and an invariant closed circle bifurcates from the positive fixed point. From the viewpoint of biology, the invariant closed curve corresponds to the periodic or quasi-periodic oscillations between host and parasitoid populations. Furthermore, it is proved that all solutions of this model are bounded, and there exist some values of the parameters such that the model has a global attractor. These theoretical results reveal the complex dynamics of the present model.     

一类捕食者-食饵系统周期正解的全局存在性

利用Ｍａｗｈｉｎ重合度理论研究了一类具有偏差变元的捕食者－食饵系统周期正解的全局存在性问题,得到了一个新的存在性定理。     

Coexistence in a simple food chain with diffusion

We show the global existence of classical positive solutions in each component of a Lotka-Volterra system with diffusion and logistic growing conditions. We are mainly interested in the search of coexistence states solving the associated elliptic problem under homogeneous Dirichlet boundary conditions.     

具毒物影响和中立型时滞两种群竞争系统的周期正解

讨论了一类具毒物影响的中立型时滞两种群竞争系统,利用重合度理论和分析技巧建立了该系统正周期解全局存在的充分条件。     

Asymptotic behaviour of a model of hierarchically structured population dynamics

 A hierarchically structured population model with a dependence of the vital rates on a function of the population density (environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass equilibrium without a nontrivial population equilibrium is shown. Received 16 February 1996; received in revised form 16 September 1996     

Convergence in almost periodic Fisher and Kolmogorov models

 We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an almost periodic global attractor is also discussed. Received: 11 November 1996 / Revised version: 8 January 1998     

Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments.

In this paper, we study the existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems. By using the method of coincidence degree and Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution of periodic n-species Lotka-Volterra competition systems with several deviating arguments and the existence of a unique globally asymptotically stable periodic solution with strictly positive components of periodic n-species Lotka-Volterra competition system with several delays. Some new results are obtained. As an application, we also examine some special cases of the system we considered, which have been studied extensively in the literature. Some known results are improved and generalized.     

一类与传染病模型有关的积分方程的定性性质

证明了一类与传染病模型有关的积分方程解的唯一性,整体存在性和当t→∞时收敛到零的若干充分条件.利用Banach不动点定理证明了存在性结果,利用一个新的积分不等式证明了收敛性结果.     

Threshold and stability results for an age-structured epidemic model

We study a mathematical model for an epidemic spreading in an age-structured population with age-dependent transmission coefficient. We formulate the model as an abstract Cauchy problem on a Banach space and show the existence and uniqueness of solutions. Next we derive some conditions which guarantee the existence and uniqueness for non-trivial steady states of the model. Finally the local and global stability for the steady states are examined.     

三种群互惠模型抛物系统解的整体存在与爆破

研究了三种群互惠模型的抛物系统,用上下解方法研究解的整体存在性与爆破问题,并给出了相应的条件.结果表明当种群自身的竞争强时解整体存在,反之则有可能爆破.     

Classical solutions and steady states of an attraction-repulsion chemotaxis in one dimension

We establish the existence of global classical solutions and non-trivial steady states of a one-dimensional attraction-repulsion chemotaxis model subject to the Neumann boundary conditions. The results are derived based on the method of energy estimates and the phase plane analysis.     

Global optimization of the Saccharomyces cerevisiae: Fermentation process

In this article, steady‐state optimization of the Saccharomyces cerevisiae fermentation process problem is performed revealing the existence of multiple optimum solutions. The globally optimum solution was determined using the NEOS global optimization solver LINDO. A branch and bound strategy (bnb20.m) and the global search and multistart algorithms in the MATLAB global optimization toolbox were successful in determining locally optimum solutions and these results are validated by plotting the objective function against the decision variables. While in some cases all the strategies were successful in obtaining the globally optimum solutions, an example is presented where the most beneficial product value, which is not a stationary point and lies on the feasible boundary, is obtained by the LINDO global optimization solver (but not the other routines) as the globally optimum solution. The Jones–Kompala model was used to model the steady‐state of the fermentation process. While several articles have been published demonstrating the existence of nonlinearities and bifurcations in this model, the challenges posed by this model to optimization has never been investigated so far and this work attempts to do so. Both dilution rate and the oxygen mass transfer coefficient were used as the decision variables individually and together. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:917–923, 2013     

Properties of the transfer functions of compartmental models

This paper is concerned with the nonlinear system of algebraic equations relating the positive parameters of a linear time-invariant compartmental model to its transfer function coefficients. The general form that these equations must take is shown, and simple necessary conditions for the existence of positive solutions are given. An immediate use of these conditions is the development of necessary conditions for a polynomial with positive coefficients to have negative roots. A method is then outlined which triangularizes the system and reduces the complete solution problem to one of finding and counting roots of a polynomial. Sufficient conditions for the existence of real and positive solutions are demonstrated.     

Existence and global asymptotic stability of positive periodic solutions of n-species delay impulsive Lotka–Volterra type systems

In this paper, the existence and global asymptotic stability of positive periodic solutions of periodic n-species Lotka–Volterra impulsive systems with several deviating arguments are studied. By using the continuation theorem of coincidence degree theory and Lyapunov–Razumikhin method, sufficient conditions are obtained. Some known results are improved and generalized.     

具有时滞的Schoener模型的全局稳定性

研究了具有时滞的Schoener竞争模型,通过构造一个合理的lyapunov函数,在一定条件下得到了该系统正解的全局稳定性．     

An analysis of facilitated-diffusion problems

This paper develops the mathematical analysis of nonlinear boundary-value problems that model the facilitated diffusion of a substrate across a membrane. The analysis includes bounds for solutions, global existence results, local uniqueness and continuity results, and estimates for parameter ranges for uniqueness of solutions.