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Clark’s Equation: A Useful Difference Equation for Population Models, Predictive Control, and Numerical Approximations
Qualitative Theory of Dynamical Systems ( IF 1.9 ) Pub Date : 2020-07-09 , DOI: 10.1007/s12346-020-00405-1
Eduardo Liz

A one-dimensional discrete-time dynamical system can be also seen as a recurrence, a difference equation, or an iteration scheme; and sometimes theoretical results come from different contexts. In this paper, I present a short survey about a particular family of one-dimensional maps that I have found in different situations. First, I introduce and explain the various motivations for the equation, and then I state some relevant results, with suitable references. Finally, I include some open problems and some words of caution about a series of recent poor-quality papers that, pretending to rediscover this equation, provide trivial results.

中文翻译:

Clark方程:人口模型,预测控制和数值逼近的有用差分方程

一维离散时间动力系统也可以看作是递归,差分方程或迭代方案。有时理论结果来自不同的环境。在本文中,我对在不同情况下发现的特定一维地图族进行了简短调查。首先,我介绍并解释了方程的各种动机,然后陈述了一些相关的结果,并给出了适当的参考。最后,对于一些近期质量较差的论文,我假装重新发现该方程式,提供了琐碎的结果,我对此提出了一些未解决的问题和警告。
更新日期:2020-07-09
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