11. Logistic analysis of economic cycles

Andžela Mialik1, Virgilijus Sakalauskas2, Kęstutis Driaunys3, Stasys Girdzijauskas4

Department of Informatics, Kaunas Faculty of Humanities, Vilnius University,
Muitines str. 8, LT-44280, Kaunas, Lithuania

1Corresponding author

E-mail: 1andzelina.m@gmail.com, 2virgilijus.sakalauskas@khf.vu.lt, 3kestutis.driaunys@khf.vu.lt, 4stasys.girdzijauskas@khf.vu.lt

(Received 16 July 2015; received in revised form 17 August 2015; accepted 24 August 2015)

Abstract. Dynamic processes, vibrations and fluctuations are the phenomena which usually accompany the development of various populations. Economic populations are no exception: capital, investments, GDP, and others. Their dynamics is connected with rather sharp fluctuations – rise and decline. Although the regularity of these fluctuations is not strictly determined, they are nevertheless considered to be periodical. The frequency of such fluctuations might be measured by nano or microhertz. It is becoming clear that basic principles of the theory of fluctuations might be applied to the research of the economic cycles. Up until today no one has provided an explanation as to why the development of economics is cyclic. While researching the peculiarities of the economic development (especially the growth phases), these reasons have been enumerated – the new economic laws have been discovered while analysing the phenomenon of financial saturation. It appears that economics is experiencing the revival (the so-called “economic resonance” or a boom) due to the saturation of the economic area (the markets) with the invested capital. Seeking the stability of the economic development, it is important to reorient the research methods from compound to simple percentage (interest). The alteration of the research instruments requires their constant updating and refinement, it also permits to achieve higher results. This article presents the economic logistic model of growth, displays its universality and potential to increase the economic harmony. The example of data analysis provided in the article visualizes the growth process under investigation.

Keywords: economic cycles, interest, logistic growth, logistical analysis, modelling, capacity, interval logistic model, fuzzy.


[1]        Meyer P. S., Yung J. W., Ausubel J. H. A primer on logistic growth and substitution: the mathematics of the Loglet lab software. Technological Forecasting and Social Change, Vol. 61, Issue 3, 1999, p. 247‑271.

[2]        Sterman J. D. Business Dynamics: Systems Thinking and Modeling for a Complex World. 2000, p. 950.

[3]        Sornette D. Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press, 2003.

[4]        Knyvienė I., Girdzijauskas S., Grundey D. Market capacity from the viewpoint of logistic analysis. Technological and Economic Development of Economy, Vol. 16, Issue 4, 2010, p. 690‑702.

[5]        Girdzijauskas S. The Logistic Theory of Capital Management: Deterministic Methods. Monograph, Transformations in Business and Economics, Vol. 7, 2008, p. 163.

[6]        Girdzijauskas S. Thoughts on economic resonance. Seminar on Shakes Scientific, Technical and Human Progress, Kaunas, 2014, p. 51‑54, (in Lithuanian).

[7]        Verhulst P. F. Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique, Vol. 10, 1838, p. 113.

[8]        Tsoularis A. Analysis of logistic growth models. Research Letters in the Information and Mathematical Sciences, Vol. 2, 2001, p. 23‑46.

[9]        Tsoularis A., Wallace J. Analysis of logistic growth models. Research Letters in the Information and Mathematical Sciences, Vol. 179, Issue 1, 2002, p. 21–55.

[10]     Bass F. M. A new product growth model for consumer durables. Management Science, Vol. 15, 1969, p. 215‑227.

[11]     Blackman A., Wade Jr., Seligman E. J., Solgliero G. C. An innovation index based upon factor analysis. Technological Forecasting and Social Change, Vol. 4, 1973, p. 301‑316.

[12]     Mahajan V., Muller E. Innovation diffusion and new product growth models in marketing. Journal of Marketing, Vol. 43, Issue 4, 1979, p. 56‑68.

[13]     Kaldasch J. The product life cycle of durable goods. http://arxiv.org/ftp/arxiv/papers/1109/ 1109.0828.pdf, 2012.

[14]     Asfiji N. S., Esfahani R. D., Dastjerdi R. B., Fakhar M. Analyzing the population growth equation in the solow growth model including the population frequency: case study. International Journal of Humanities and Social Science, Vol. 2, Issue 10, 2012.

[15]     Grubler A. Introduction to Diffusion Theory. Vol. 3: Models, Case Studies and Forecasts of Diffusion. Chapmanand Hall, London, UK, 1991, p. 3‑52.

[16]     Grubler A., Nakicenovic N. Long waves, technology diffusion and, substitution. http://www.iiasa.ac.at/Admin/PUB/Documents/RP-91-017.pdf, http://www.ijhssnet.com/journals/ Vol_2_No_10_Special_Issue_May_2012/16.pdf, 2012.

[17]     Boretos G. P. The future of the global economy. Technological Forecasting and Social Change, Vol. 76, 2009, p. 316‑326.

[18]     Girdzijauskas S., Streimikiene D., Mialik A. Economic growth, capitalism and unknown economic paradoxes. Sustainability, Vol. 4, 2012, p. 2818‑2837.

[19]     Ragulskis K. Mechanisms Based on a Vibrating: Questions of Dynamics and Stability. Kaunas, 1963, p. 232, (in Russian).

[20]     Kunicyna N. N. Cycle types in economy dynamics. North-Caucasus Federal University, Science Journal “Ekonomika”, Vol. 5, 2002, p. 129, (in Russian).

[21]     Rogers E. M. Diffusion of innovations. 5th Edition. The Free Press, New York, 2003.

[22]     Stock J. H., Watson M. W. Business Cycles, Indicators, and Forecasting. University of Chicago Press for NBER, 1993, p. 348.

[23]     Artis M. I., Bladen-Hovell R. C., Zhang W. Turning points in the international business cycle: an analysis of the OECD leading indicators for the G-7 countries. OECD Economic Studies, 1955, p. 125‑165.

[24]     Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society, Vol. 115, 1825, p. 513‑585.

[25]     Fisher J. C., Pry R. H. A simple substitution model of technological change. Technological Forecasting and Social Change, Vol. 3, 1971, p. 75‑88.

[26]     Mialik A. Logistic Method to Indicate Unsustainable Growth Situations. Doctoral Dissertation, Vilnius, 2014.

[27]     Efron B., Tibshirani R. J. An Introduction to the Bootstrap, Vol. 57. CRC Press, 1994.

[28]     Real Estate Charts. United States House Prices. http://www.jparsons.net/housingbubble, 2013.

[29]     Nguyen J. 4 Key Factors That Drive the Real Estate Market. http://www.investopedia.com/ articles/mortages-real-estate/11/factors-affecting-real-estate-market.asp, 2011.

[30]     Pettinger T. Factors That Affect the Housing Market. http://www.economicshelp.org/ blog/377/housing/factors-that-affect-the-housing-market, 2013.

Cite this article

Mialik Andžela, Sakalauskas Virgilijus, Driaunys Kęstutis, Girdzijauskas Stasys Logistic analysis of economic cycles. Mathematical Models in Engineering, Vol. 1, Issue 2, 2015, p. 83‑95.


Mathematical Models in Engineering. December 2015, Volume 1, Issue 2

© JVE International Ltd. ISSN Print 2351-5279, ISSN Online 2424-4627, Kaunas, Lithuania