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The study is is an urgent warning on the Earth Day 2020 to prevent the blast of the COVID-19 pandemic to chaotic apocalypse. It is shown that the pandemic equations become unstable at reproduction numbers above 3.5, which could reflect in a chaotic catastrophe. R.I.P. Robert M. May, Baron May of Oxford.
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An urgent attempt is made to apply thermodynamic laws to the Greek society. A negative social entropy production is predicted, which could be achieved either by a military regime or by a restrictive agreement with the creditors of Greece.
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First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hiearchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.
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A large class of recursion relationsx n + 1 = [`(x)]\bar x . With f([`(x)]) - f(x) ~ | x - [`(x)] |z (for| x - [`(x)] |f(\bar x) - f(x) \sim \left| {x - \bar x} \right|^z (for\left| {x - \bar x} \right| sufficiently small),z > 1, the universal details depend only uponz. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio[`(x)]\bar x exists; – n R~ –n ( = 4.669201609103... forz = 2). The numbers and have been computationally determined for a range ofz through their definitions, for a variety off's for eachz. We present a recursive mechanism that explains these results by determiningg * as the fixed-point (function) of a transformation on the class off's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.
The first of three volumes, nos. 5-7 in the Newton Institute series, from the research programme on "Epidemic Models: their structure and relation to data" at the Isaac Newton Institute, Jan-Jun 1993.
The World knows an apocalyptic pandemic is coming
  • L Garrett
Garrett L. (2019) The World knows an apocalyptic pandemic is coming, Washington, Foreign Policy