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Clark’s Equation: A Useful Difference Equation for Population Models, Predictive Control, and Numerical Approximations

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Abstract

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.

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Acknowledgements

The author acknowledges the support of the research grant MTM2017–85054–C2–1–P (AEI/FEDER, UE).

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  1. Departamento de Matemática Aplicada II, Universidade de Vigo, 36310, Vigo, Spain

    Eduardo Liz

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  1. Eduardo Liz
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Liz, E. Clark’s Equation: A Useful Difference Equation for Population Models, Predictive Control, and Numerical Approximations. Qual. Theory Dyn. Syst. 19, 71 (2020). https://doi.org/10.1007/s12346-020-00405-1

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