英文标题：
《Logistic map with memory from economic model》
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作者：
Valentina V. Tarasova, Vasily E. Tarasov
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最新提交年份：
2017
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英文摘要：
  A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their values at that time, but also on their values at previous times. For the mathematical description of the memory effects, we use the theory of derivatives of non-integer order. Crises are considered as sharp splashes (bursts) of the price, which are mathematically described by the delta-functions. Using the equivalence of fractional differential equations and the Volterra integral equations, we obtain discrete maps with memory that are exact discrete analogs of fractional differential equations of economic processes. We derive logistic map with memory, its generalizations, and \"economic\" discrete maps with memory from the fractional differential equations, which describe the economic natural growth with competition, power-law memory and crises.
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中文摘要：
提出了考虑记忆和危机影响的物流增长经济模型的推广。记忆效应是指任何给定时间的经济因素和参数不仅取决于当时的值，还取决于以前的值。对于记忆效应的数学描述，我们使用了非整数阶导数理论。危机被认为是价格的剧烈波动（爆发），这在数学上由delta函数描述。利用分数阶微分方程和Volterra积分方程的等价性，我们得到了具有记忆的离散映射，这些映射是经济过程分数阶微分方程的精确离散类似物。我们从分数阶微分方程中导出了带记忆的logistic映射及其推广，以及带记忆的“经济”离散映射，它们描述了具有竞争、幂律记忆和危机的经济自然增长。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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