Study of critical phenomena in economic systems using a model of damped oscillations

Danylchuk, Hanna; Kibalnyk, Lіubov; Serdiuk, Olexandr

doi:10.1051/shsconf/20196506008

Cited by 4 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is necessary to allocate several scientific articles focusing the modeling of financial markets and identification of crisis periods with the use of economic and other interdisciplinary methods. These articles prove the effectiveness of entropy methods, network models, the Heisenberg uncertainty principle, scale-dependent Lyapunov indicators and other approaches for detecting and predicting crisis phenomena (See, e.g., Soloviev and Saptsin, 2011;Soloviev and Belinskij, 2018;Soloviev et al, 2019;Danylchuk et al, 2016;Danylchuk et al, 2019;Danylchuk et al, 2020).…”

Section: Introductionmentioning

confidence: 86%

Modeling of Crisis Phenomena in Regional Stock Markets by Wavelet-Entropy Method

Danylchuk¹,

Kibalnyk²

2021

MDES

Self Cite

View full text Add to dashboard Cite

The article reflects the results of a study on modelling regional stock markets using wavelet entropy. Particular attention is paid to periods of crises as special states of markets. Countries with the developed economies were selected for the study, namely, the United States, United Kingdom, Germany, France, China, Japan and Hong Kong. The values of stock indices of regional stock markets were used as a statistical base. The research period is from 2015 to 2021. The aim of the article is to monitor the current state of markets and to demonstrate the possibilities of using the wavelet entropy index as a precursor of crisis phenomena. The wavelet entropy method was used. All calculations were performed in the Matlab environment - a system for modeling nonlinear dynamical systems. The results of the study demonstrate the absence of crisis phenomena in these markets as of April 2021. It is shown that the use of wavelet entropy as a precursor indicator is reasonable. In particular, the reaction of stock markets to such crisis situations as the COVID-19 pandemic as well as other socio-political events is shown. Based on the results of calculations, conclusions are made about the current state of stock markets of the studied countries. All stock market participants, investors, and relevant ministries to develop effective strategies can use the results obtained, as well as the method in general.

show abstract

Section: Introductionmentioning

confidence: 86%

Modeling of Crisis Phenomena in Regional Stock Markets by Wavelet-Entropy Method

Danylchuk¹,

Kibalnyk²

2021

MDES

Self Cite

View full text Add to dashboard Cite

show abstract

“…The variable order q (t) of the fractional derivative determines the intensity of energy dissipation in the oscillatory system. If this order is constant and equal to one, then the Cauchy problem (3) becomes the Cauchy problem for the classical Duffing oscillator [4] .…”

Section: Problem Statement and Numerical Solutionmentioning

confidence: 99%

“…Hereditarity is a property of a dynamic system in which its current state depends on previous states. Hereditary dynamical systems find their application in hereditary mechanics [2], biology [3], economics [4] and other fields of knowledge.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of Fractional Duffing Oscillator with Variable Memory

Kim

Parovik

2020

Mathematics

View full text Add to dashboard Cite

The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann–Liouville type by a discrete analog—the fractional derivative of Grunwald–Letnikov. The adequacy of the numerical scheme is verified using specific examples. Using a numerical algorithm, oscillograms and phase trajectories are constructed depending on the values of the model parameters. Chaotic regimes of the Duffing fractional oscillator are investigated using the Wolf–Bennetin algorithm. The forced oscillations of the Duffing fractional oscillator are investigated using the harmonic balance method. Analytical formulas for the amplitude-frequency, phase-frequency characteristics, and also the quality factor are obtained. It is shown that the fractional Duffing oscillator possesses different modes: regular, chaotic, multi-periodic. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.

show abstract

“…Models of oscillatory systems (oscillators) are used in various fields of knowledge from mechanics to economics and biology [1,2,3]. From the point of view of mathematics, these models are usually described using ordinary differential equations of the second order and the corresponding initial conditions, i.e.…”

Section: Introductionmentioning

confidence: 99%

Application of the Adams-Bashfort-Mowlton method to the numerical study of linear fractional oscillators models

Parovik¹

2021

International Uzbekistan-Malaysia Conference on “Computational Models and Technologies (Cmt2020)”: Cmt2020

View full text Add to dashboard Cite

The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A method based on an explicit nonlocal finite-difference scheme (ENFDS) and the Adams-Bashfort-Moulton (ABM) method are considered as tools for numerical analysis. An analysis of the errors of the methods is carried out, it is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method.

show abstract

Study of critical phenomena in economic systems using a model of damped oscillations

Cited by 4 publications

References 18 publications

Modeling of Crisis Phenomena in Regional Stock Markets by Wavelet-Entropy Method

Modeling of Crisis Phenomena in Regional Stock Markets by Wavelet-Entropy Method

Mathematical Model of Fractional Duffing Oscillator with Variable Memory

Application of the Adams-Bashfort-Mowlton method to the numerical study of linear fractional oscillators models

Contact Info

Product

Resources

About