Logistic map with memory from economic model

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....

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Tarasova, Valentina V, Tarasov, Vasily E
Format: Article
Language:English
Subjects:
Differential equations
Economic analysis
Economic factors
Economic models
Mathematical models
Volterra integral equations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1712.09092