共查询到20条相似文献,搜索用时 15 毫秒
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《Mathematical biosciences》1986,78(2):217-245
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. 相似文献
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本文考虑了两种群具有脉冲效应的非自治Lotka-Valterra竞争系统.运用比较定理和李雅普诺夫函数法,建立了系统的持久性和渐近行为的充分条件. 相似文献
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Charles Tier 《Journal of mathematical biology》1982,12(1):53-71
Three diffusion models are formulated for the evolution of a diploid population with K alleles at one locus with completely symmetric mutation and random genetic drift, a variable-environment, and all the above mechanisms. For the diallelic case, the transient behavior is studied by solving the corresponding diffusion equations by an asymptotic method valid for short time intervals. The transient behavior of the three models is compared for the case when their stationary distributions are identical. The expected amount of heterozygosity is computed using the asymptotic solution and is compared to an exact result. The asymptotic results are extended to the general case with K alleles at the locus for the symmetric mutation and variable-environment models.Research supported by the National Science Foundation under Grant MCS 79-01718 相似文献
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研究了一类具有扰动的非自治Kolmogorov模型的渐近性.得到了扰动系戎的解渐近稳定的若干充分条件. 相似文献
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L J Allen 《Mathematical biosciences》1989,95(2):179-187
A density-dependent Leslie matrix model introduced in 1948 by Leslie is mathematically analyzed. It is shown that the behavior is similar to that of the constant Leslie matrix. In the primitive case, the density-dependent Leslie matrix model has an asymptotic distribution corresponding to the logistic equation. However, in the imprimitive case, the asymptotic distribution is periodic, with period depending on the imprimitivity index. 相似文献
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The analysis of ecological models often focuses on their asymptotic behavior, but there is increasing recognition that it is important to understand the role of transient behavior. By introducing a time delay into a model of coral-algal interactions in Caribbean coral reefs that exhibits alternative stable states (a favorable coral rich state and a degraded coral-depleted state), we demonstrate the criticality of understanding the basins of attraction for stable equilibria in addition to the systems' asymptotic behavior. Specifically, we show that although the introduction of a time delay into the model does not change the asymptotic stability of the stable equilibria, there are significant changes to their basins of attraction. An understanding of these effects is necessary when determining appropriate reef management options. We then demonstrate that this is a general phenomenon by considering similar behavior underlying the changes in the basins of attraction in a simple Lotka-Volterra model of competition. 相似文献
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In this paper, the global asymptotic behavior of a chemostat model with Beddington-DeAngelis functional response is studied. The conditions for the global asymptotical stability of the model with time delays are obtained via monotone dynamical systems. Our results demonstrate that those time delays affect the competitive outcome of the organisms. 相似文献
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一类竞争扩散方程组在Neumann边条件下解的渐近行为 总被引:1,自引:0,他引:1
本文主要采用比较方法讨论了一类竞争扩散方程组在Neumann边条件下解的渐近行为,得到了解的稳定性区域. 相似文献
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N Mantel 《Biometrics》1985,41(3):777-783
In minimum chi-square logit or probit analysis of quantal bioassay data, a requirement for proper asymptotic behavior of the estimates made is that test-group sizes get indefinitely large. Inconsistent estimates result if group sizes are small, however numerous the groups. Maximum likelihood estimates do not show this inconsistent behavior, even if all the many group sizes are only unity. The inconsistent behavior for minimum chi-square results from a bias toward 0.5 for response probabilities. At 0.5 the binomial variance is at a maximum of 0.25, so tending to minimize the calculated value of chi square. The principle of minimum chi-square should not be confused with the principle of least squares. 相似文献
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Paul J. Polansky 《Journal of mathematical biology》1978,6(4):333-342
Summary We consider a two niche model of two populations interacting through migration and undergoing exponential growth. Random effects
enter through demographic stochasticity or randomization of the growth rates. Conditions for the moments to converge to zero
or infinity are found. In addition, the asymptotic behavior of the paths of the diffusion process is characterized. 相似文献
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This paper studies the dynamics of a mathematical model of a continuously reproducing diploid population with two alleles at one locus. The dependent variables are allele frequency and population density. If the genotype fitnesses are frequency and density dependent, the stability of equilibria is related to the geometry of the zero allele fitness curves. The asymptotic behavior of solutions where fitness is only density dependent is contrasted to the asymptotic behavior where fitness is frequency and density dependent. A parameterized family of fitness functions giving a Hopf bifurcation and limit cycles is investigated analytically and numerically. 相似文献
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Marcos R. Betancourt 《Biopolymers》2016,105(6):312-323
Bond‐orientational correlations for finite‐length homopolypeptides and a selected group of denatured proteins are obtained by numerical simulations using a polypeptide model with a potential of mean force. These correlations characterize the stiffness of the polypeptide backbone and are generally described by either an exponential or a power‐law decay in the asymptotic limit. However, for finite length polypeptides and unfolded proteins the correlations significantly deviate from either single exponential or power‐law behavior. A heuristic model is developed to analyze the correlations of homopolypeptides, which depends on the chain length and the side‐chain properties. The model contains power‐law and multi‐exponential terms, the latter which could be interpreted as local persistence lengths. In the asymptotic limit, the model reduces to the expected power‐law behavior. Simulations of denatured proteins show that the power‐law behavior of the correlations is significantly suppressed and only the multi‐exponential term is needed to model the correlations. In addition, average persistence lengths (ranging from 2.0 to 2.5 nm) are obtained from the correlations by fitting single exponentials and shown to be in general agreement with experiments, which also assume single exponential decay. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 312–323, 2016. 相似文献
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本文讨论一类不满足所谓的拟单调条件的反应扩散方程组的初边值问题.应用谱论和单调性方法证明了问题解的存在唯一性和平衡解的渐近稳定性.并进一步讨论了生态学中n种群单食物链模型的第二初值问题,得到了问题的非负平衡解的存在性和渐近性以及相应的吸引区域. 相似文献
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M Andersen 《Mathematical biosciences》1991,104(1):135-157
Integrodifference equations may be used as models of populations with discrete generations inhabiting continuous habitats. In this paper integrodifference equation models are formulated for annual plant populations without a seed bank; these models differ in the stage of the life cycle at which intraspecific competition acts to reduce vital rates. The models exhibit a sequence of period-doubling bifurcations leading to chaotic spatial and temporal behavior. The behavior of the models when modal dispersal distances are at the origin is compared with their behavior when these distances are displaced away from the origin. The models are capable of predicting stable, cyclical, and chaotic asymptotic behavior. They also predict that the variance of dispersal distances is an important indicator of the colonizing ability of a species. 相似文献