Title: Relaxation oscillations properties in Goodwin's business cycle model

Authors: Anna Antonova; Svyatoslav Reznik; Michail Todorov

Addresses: Institute of Economics and Management, National Aviation University, 1 Kosmonauvta Komarova Ave., 03058 Kyiv, Ukraine ' Institute for Nuclear Research, National Academy of Sciences of Ukraine, 47 Prospekt Nauky, 03680, Kyiv, Ukraine ' Faculty of Applied Mathematics and Computer Science, Technical University of Sofia, 8 Kliment Ohridski Blvd., 1000 Sofia, Bulgaria

Abstract: We consider Goodwin's time delay model of the business cycle described by neutral delay differential equation with fixed investment time lag. We investigate the properties of relaxation (sawtooth) oscillations, detected experimentally by Strotz et al. (1953). We show that the shape of relaxation fluctuations (amplitude, average value of income over the period of oscillation, time of income rise and fall) depends on the initial function. We also present an analytical sawtooth solution of the delay equation obtained by the method of steps. Finally, we show the existence of irregular dynamics of income.

Keywords: Goodwin; business cycle models; delay equation; limit cycle; sawtooth oscillations; relaxation oscillations; modelling; time delay models; income irregular dynamics.

DOI: 10.1504/IJCEE.2013.058495

International Journal of Computational Economics and Econometrics, 2013 Vol.3 No.3/4, pp.146 - 163

Received: 04 Dec 2012
Accepted: 03 May 2013

Published online: 31 Dec 2013 *

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