具有和不具有Allee效应的双斑块种群模型的稳态动力学

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2023-09-22 DOI:10.5206/mase/16474
Laurence Ketchemen Tchouaga, Frithjof Lutscher
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引用次数: 0

摘要

大多数生物种群居住在由许多不同质量的不同斑块组成的景观中。不同的物种在运动行为、栖息地偏好和生长速度上存在差异。历史上,人口动态的数学模型做出了许多简化的假设,例如单一斑块或均匀景观。最近的模型已经开始实现景观异质性和个体运动特征,但其中许多是基于逻辑增长和零状态的线性分析。我们考虑一个具有更一般的生长函数的双补丁模型,可以包括Allee效应。证明了稳态的存在性,并对其定性行为进行了分类。在一些特殊情况下,我们显式地计算了它们的稳定性,并利用这些结果给出了系统呈现双稳定性的条件,即局部稳定状态的共存。我们还研究了与生境斑块大小有关的分岔,并给出了向前和向后分岔的条件。
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Steady-state dynamics in a two-patch population model with and without Allee effect
Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
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