A unifying framework for chaos and stochastic stability in discrete population models
A unifying framework for chaos and stochastic stability in discrete population models
复制标题
离散总体模型中混沌和随机稳定性的统一框架
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
G. Högnäs
中科院分区：
文献类型：
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作者：
M. Vellekoop;G. Högnäs
摘要：在本文中，我们提出了一个离散时间一维马尔可夫人口模型的一般框架，它是基于人口动力学的两个基本前提。 我们发现，这个框架结合了早期的人口模型，如Ricker和Hassell模型，以及关于密度依赖结构的实验观察。种群动力学的两个基本前提足以保证模型在自然增长和密度依赖反馈的高值下表现出混沌行为，并且这种观察与模型的特定结构无关。我们还研究了这些模型时，人口的环境随机变化，并解决在什么条件下，我们可以找到一个不变的概率分布的人口正在考虑的问题。这种随机稳定性的充分条件，我们得出的一些兴趣，因为研究这些随机人口过程的某些统计特性可能只有可能的过程收敛到这样一个不变的分布。
Abstract. In this paper we propose a general framework for discrete time one-dimensional Markov population models which is based on two fundamental premises in population dynamics. We show that this framework incorporates both earlier population models, like the Ricker and Hassell models, and experimental observations concerning the structure of density dependence. The two fundamental premises of population dynamics are sufficient to guarantee that the model will exhibit chaotic behaviour for high values of the natural growth and the density-dependent feedback, and this observation is independent of the particular structure of the model. We also study these models when the environment of the population varies stochastically and address the question under what conditions we can find an invariant probability distribution for the population under consideration. The sufficient conditions for this stochastic stability that we derive are of some interest, since studying certain statistical characteristics of these stochastic population processes may only be possible if the process converges to such an invariant distribution.