Periodicity and boundedness of solutions of generalized differential equations of growth

Sufficient conditions are given for the existence of periodic solutions of differential equations, having as special cases the equations used to describe the competition between two species. The Poincaré bifurcation theory is used to secure one set of conditions, and another set of conditions is secured through a generalization of a method of V. Volterra. The question of boundedness is considered and conditions implying boundedness and conditions implying that populations are bounded away from zero are given. Several integrable classes of systems are discovered and a particular example having periodic solutions is examined in detail. This research was supported by the Air Force Office of Scientific Research under Grant 62-207.     

Dynamics of a food-limited population model incorporating nonlocal delays on a finite domain

 In this paper we model and analyse nonlocal spatial effects, induced by time delays, in a diffusion model for a single species confined to a finite domain. The nonlocality, a weighted average in space, arises when account is taken of the fact that individuals have been at different points in space at previous times. We show how to correctly derive the spatial averaging kernels for finite domain problems, generalising the ideas of other investigators who restricted attention to the simpler case of an infinite domain. The resulting model is then analysed and results established on linear stability, boundedness, global convergence of solutions and bifurcations. Received: 29 August 2000 / Revised version: 6 March 2001 / Published online: 7 December 2001     

Comparing functional responses in predator-infected eco-epidemics models

The current paper deals with the mathematical models of predator–prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator–prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results.     

Analysis of a mathematical model for transport of I-albumin

The hypotheses and results given are motivated by the study of the distribution of albumin in man which represents a class of delay-differential systems. The approach used is to study the behavior of the solutions of nonlinear delay-differential systems with variable coefficients under the assumptions of continuity and boundedness of coefficients. The criterions are conditions on the roots of a certain “quasi-polynomial”, i.e., a polynomial in a variable and exponential of that variable. These criterions bear a resemblance to the ones in the case of constant coefficients and retardations and are applicable to this case also. The method is based on Lyapunov type functional with appropriate properties.     

Initial/boundary-value problems of tumor growth within a host tissue

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori non-negativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.     

具有时滞的微分方程解的振动与非振动

本文主要考虑了具有时滞的微分方程（记作（A）．在文章的第一部分,主要研究了系统（A）的一致持久性,（A）的满足条件（0．4）的解的一致有界和一致最终有界;在第二部分主要研究了界的振动与非振动性。     

一类捕食—食饵动力系统的定性分析

本文对一类形式广泛的捕食-食饵动力系统进行了定性研究，获得了确保此生态系统的所有解有界及极限环存在与唯一的若干充分条件，并给出了所获结论在生态学上的意义。     

Global behavior of solutions of a periodically forced Sigmoid Beverton-Holt model

Our aim in this paper is to investigate the boundedness, the extreme stability, and the periodicity of positive solutions of the periodically forced Sigmoid Beverton-Holt model: [Formula: see text] where {a ( n )} is a positive periodic sequence with period p and δ>0. In the special case when δ=1, the above equation reduces to the well-known periodic Pielou logistic equation which is known to be equivalent to the periodically forced Beverton-Holt model.     

The uniqueness of wave solutions for the deterministic non-reducible n-type epidemic

In a recent paper, [8], we investigated the existence of wave solutions for a model of the deterministic non-reducible n-type epidemic. In this paper we first prove two properties left as an open question in that paper. The uniqueness of the wave solutions at all speeds for which a wave solution exists is then established. Only an exceptional case is not covered.     

The stabilizing effect of a random environment

It is shown that the lottery competition model permits coexistence in a stochastic environment, but not in a constant environment. Conditions for coexistence and competitive exclusion are determined. Analysis of these conditions shows that the essential requirements for coexistence are overlapping generations and fluctuating birth rates which ensure that each species has periods when it is increasing. It is found that a species may persist provided only that it is favored sufficiently by the environment during favorable periods independently of the extent to which the other species is favored during its favorable periods.Coexistence is defined in terms of the stochastic boundedness criterion for species persistence. Using the lottery model as an example this criterion is justified and compared with other persistence criteria. Properties of the stationary distribution of population density are determined for an interesting limiting case of the lottery model and these are related to stochastic boundedness. An attempt is then made to relate stochastic boundedness for infinite population models to the behavior of finite population models.     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

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.     

An analytic solution to the Förster energy transfer problem in two dimensions.

An analytic solution of the F?rster energy transfer problem in two dimensions is presented for the case in which the orientation factor is independent of the donor-acceptor distance, and both the donors and acceptors are randomly distributed in a plane. A general solution based on the method of F?rster is possible since all distances are measured in units of R0. The analytic solution is extended to the cases of donors embedded in structures that exclude acceptors, and donors that bind acceptors. The validity of the analytic solutions is demonstrated by comparison with numerical simulation calculations. Numerical approximations to the exact solutions are given for ease of computation. Specific applications to the case of fluorescence quenching of a membrane-bound donor by membrane-bound acceptors are presented.     

Stability in chemostat equations with delayed nutrient recycling

The growth of a species feeding on a limiting nutrient supplied at a constant rate is modelled by chemostat-type equations with a general nutrient uptake function and delayed nutrient recycling. Conditions for boundedness of the solutions and the existence of non-negative equilibria are given for the integrodifferential equations with distributed time lags. When the time lags are neglected conditions for the global stability of the positive equilibrium and for the extinction of the species are provided. The positive equilibrium continues to be locally stable when the time lag in recycling is considered and this is proved for a wide class of memory functions. Computer simulations suggest that even in this case the region of stability is very large, but the solutions tend to the equilibrium through oscillations.Work performed within the activity of the research group Equazioni di evoluzione e applicazioni Fisico-Matematiche, MPI (Italy), and under the auspices of GNFM, CNR (Italy)     

非自治LOTKA-VOLTERRA生态系统的有界性及周期解的存在性

本文利用图论和Liapunov方法研究了非自治LOTKA-VOLTERRA生态系统的有界性和周期解的存在性,得到了一些新的结果．     

Genetic coupling in mate recognition systems: what is the evidence?

Genetic coupling and coevolution of male and female components have been seen as alternative solutions to the problem of maintaining coordination between the sexes during evolutionary divergence of mate recognition systems. The evidence supposed to provide a distinction between these alternatives is reviewed. In most cases the data are inadequate, but in two examples coupling is clearly absent and in no case is it firmly established as the explanation for the maintenance of coordination. The distinction may only be useful in systems controlled by a few major loci as opposed to polygenic systems.     

Are bowing of long tubular bones and preaxial polydactyly signs of the Meckel syndrome?

We describe four cases with signs resembling those of Meckel syndrome. Two cases demonstrated postaxial polydactyly; one case, preaxial polydactyly; and one case, pre- and postaxial polydactyly. Since there is at least one other reported case with preaxial polydactyly, it may be a rare sign of the Meckel syndrome. In all four cases, various degrees of bowing of the long tubular bones were observed. Since at least two cases exhibited typical Meckel syndrome and since in a few further reported cases X-ray examination revealed bowing of long tubular bones, this sign is considered to be a further, hitherto not well recognized sign of the Meckel syndrome, and not grounds for delineation of a new syndrome. An extensive review of the literature revealed, that shortened and bowed extremities may be present in about one-sixth of all cases with Meckel syndrome.     

The effect of dispersal on single-species nonautonomous dispersal models with delays

In this paper, single-species nonautonomous dispersal models with delays are considered. An interesting result on the effect of dispersal for persistence and extinction is obtained. That is, if the species is persistent in a patch then it is also persistent in all other patches; if the species is permanent in a patch then it is also permanent in all other patches; if the species is extinct in a patch then it is also extinct in all other patches. Furthermore, some new sufficient conditions for the permanence and extinction of the species in a patch are established. The existence of positive periodic solutions is obtained in the periodic case by employing Teng and Chen's results on the existence of positive periodic solutions for functional differential equations. Received: 26 June 2000 / Revised version: 6 October 2000 / Published online: 10 April 2001     

On the kinetic depth effect

The problem of the kinetic depth effect is revisited. We study how many points in how many views are necessary and sufficient to recover structure. The constraints in the cases where the velocities of the image points are known, and the positions of the image points are known with the correspondence between them established, are different and they have to be studied separately. In the case of two projections of any number of points there are infinitely many solutions, but if we regularize the problem we get a unique solution under some assumptions. Finally, an algorithm is discussed for learning this particular kind of regularization.