Study of irregular dynamics in an economic model : attractor localization and Lyapunov exponents
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
Published inChaos, Solitons and Fractals
DisciplineTietotekniikkaLaskennallinen tiedeComputing, Information Technology and MathematicsMathematical Information TechnologyComputational ScienceComputing, Information Technology and Mathematics
© 2021 The Author(s). Published by Elsevier Ltd.
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). ...
Publication in research information system
MetadataShow full item record
Additional information about fundingThis paper was prepared with the support by the Leading Scientific Schools of Russia: project NSh-2624.2020.1 (sections 3, 4). Authors from the St.Petersburg State University acknowledge support from St.Petersburg State University grant Pure ID 75207094 (section 1,2).
Showing items with similar title or keywords.
Alexeeva, Tatyana A.; Barnett, William A.; Kuznetsov, Nikolay V.; Mokaev, Timur N. (Elsevier, 2020)Forecasting and analyses of the dynamics of financial and economic processes such as deviations of macroeconomic aggregates (GDP, unemployment, and inflation) from their long-term trends, asset markets volatility, etc., ...
Kuznetsov, N. V.; Mokaev, T. N.; Kuznetsova, O. A.; Kudryashova, E. V. (Springer, 2020)On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global ...
Alexeeva, T.A.; Barnett, W.A.; Kuznetsov, N.V.; Mokaev, T.N. (Elsevier, 2020)Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control ...
Numerical analysis of dynamical systems : unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension Kuznetsov, Nikolay; Mokaev, Timur (IOP Publishing, 2019)In this article, on the example of the known low-order dynamical models, namely Lorenz, Rössler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz ...
Wang, Ning; Zhang, Guoshan; Kuznetsov, Nikolay; Bao, Han (Elsevier BV, 2021)The first hidden chaotic attractor was discovered in a dimensionless piecewise-linear Chua’s system with a special Chua’s diode. But designing such physical Chua’s circuit is a challenging task due to the distinct slopes ...