A1 Journal article (refereed)
Study of irregular dynamics in an economic model : attractor localization and Lyapunov exponents (2021)

Alexeeva, T. A., Kuznetsov, N. V., & Mokaev, T. N. (2021). Study of irregular dynamics in an economic model : attractor localization and Lyapunov exponents. Chaos, Solitons and Fractals, 152, Article 111365. https://doi.org/10.1016/j.chaos.2021.111365

JYU authors or editors

Publication details

All authors or editors: Alexeeva, Tatyana A.; Kuznetsov, Nikolay V.; Mokaev, Timur N.

Journal or series: Chaos, Solitons and Fractals

ISSN: 0960-0779

eISSN: 1873-2887

Publication year: 2021

Volume: 152

Article number: 111365

Publisher: Elsevier

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1016/j.chaos.2021.111365

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/77952

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2107.13907

Abstract

Cyclicality and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global attractor and study limiting dynamics of the model. We estimate the Lyapunov exponents and get the exact formula for the Lyapunov dimension of the global attractor of this model analytically. With the help of delayed feedback control (DFC), the possibility of transition from irregular limiting dynamics to regular periodic dynamics is shown to solve the problem of reliable forecasting. At the same time, we demonstrate the complexity and ambiguity of applying numerical procedures to calculate the Lyapunov dimension along different trajectories of the global attractor, including unstable periodic orbits (UPOs).

Keywords: economic models; economic forecasts; seasonal variations; dynamical systems; attractors; chaos theory

Free keywords: Lyapunov exponents; Lyapunov dimension; Unstable periodic orbit; Absorbing set; Mid-size firm model

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2021

JUFO rating: 1