DIFFUSIVE LOGISTIC EQUATIONS WITH INDEFINITE WEIGHTS - POPULATION-MODELS IN DISRUPTED ENVIRONMENTS
DIFFUSIVE LOGISTIC EQUATIONS WITH INDEFINITE WEIGHTS - POPULATION-MODELS IN DISRUPTED ENVIRONMENTS
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DOI：
10.1017/s030821050001876x
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发表时间：
1989-01-01
影响因子：
1.3
通讯作者：
COSNER, C
中科院分区：
文献类型：
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作者：
CANTRELL, RS;COSNER, C
在Ω ×（0,∞）中，通过扩散logistic方程ut = d Δu + [m(x) - cu]u来模拟居住在强异质环境中的种群的动态，其中u代表种群密度，c, d >分别是描述拥挤和种群扩散速率的极限效应的常数，m(x)描述种群的局部增长率。如果环境∞是有界的，并且被不适合居住的区域包围，则u = 0 on∂∞x（0,∞）。生长速率m(x)在有利生境为正，在不利生境为负。分析的目的是确定有利和不利生境的空间安排如何影响被模拟的人口。这些模型被证明具有一个独特的，稳定的，积极的稳态（意味着人口的持久性）提供l/d>，其中是问题的主要正特征值- Δϕ=λm(x)ϕ in Χ，ϕ=0 on∂Ω。对m的依赖性的分析表明，有利生境和不利生境紧密混合的环境对种群的影响比具有大面积均匀有利生境的环境更差。当扩散速率d↓0为极限时，溶液趋向于m(x)/c的正部分，当m为不连续时，形成内部过渡层。分析使用分岔和延拓方法、特征值的变分表征、上下解技术和奇异摄动理论。
The dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form ut = d Δu + [m(x) — cu]u in Ω × (0, ∞), where u represents the population density, c, d > 0 are constants describing the limiting effects of crowding and the diffusion rate of the population, respectively, and m(x) describes the local growth rate of the population. If the environment ∞ is bounded and is surrounded by uninhabitable regions, then u = 0 on ∂∞× (0, ∞). The growth rate m(x) is positive on favourablehabitats and negative on unfavourable ones. The object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled. The models are shown to possess a unique, stable, positive steady state (implying persistence for the population) provided l/d> where is the principle positive eigenvalue for the problem — Δϕ=λm(x)ϕ in Χ,ϕ=0 on ∂Ω. Analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat. In the limit as the diffusion rate d ↓ 0, the solutions tend toward the positive part of m(x)/c, and if m is discontinuous develop interior transition layers. The analysis uses bifurcation and continuation methods, the variational characterisation of eigenvalues, upper and lower solution techniques, and singular perturbation theory.