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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


A Hierarchy of Out-of-Equilibrium Actor-Based System-Dynamic Nonlinear conomic Models

Discontinuity, Nonlinearity, and Complexity 3(3) (2014) 303--318 | DOI:10.5890/DNC.2014.09.007

Dmitry V. Kovalevsky$^{1}$,$^{2}$,$^{3}$, Klaus Hasselmann$^{4}$,$^{5}$

$^{1}$ Nansen International Environmental and Remote Sensing Centre, 14th Line 7, office 49, Vasilievsky Island, 199034 St. Petersburg, Russia

$^{2}$ Saint Petersburg State University, Ulyanovskaya 3, 198504 St. Perersburg, Russia

$^{3}$ Nansen Environmental and Remote Sensing Center, Thormøhlens gate 47, N-5006 Bergen, Norway

$^{4}$ Max Planck Institute for Meteorology, Bundesstraße 53, 20146 Hamburg, Germany

$^{5}$ Global Climate Forum, Neue Promenade 6, 10178 Berlin, Germany

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The actor-based system-dynamic approach to macroeconomic modeling is illustrated for a simple model hierarchy consisting of a basic twodimensional model with several alternative three-dimensional extensions. The hierarchy is based on an out-of-equilibrium approach: market clearing is not assumed, supply is not equal to demand, and there exists a stock of unsold goods. Depending on actor behaviour, the models exhibit stable exponential growth or instabilities leading to nonlinear oscillations or economic collapse. In most cases, the simplicity and tractability of the models enables analytical solutions. The examples serve as illustration of more realistic models developed within the Multi-Actor Dynamic Integrated Assessment Model System (MADIAMS) to assess the long-term impacts of climate mitigation policies.


An earlier version of this paper (Ref. [36]) appeared as an (unpublished) manuscript for GSS Preparatory Workshop for the 3rd Open Global Systems Science Conference (2014) (29-30 October 2013, Global Climate Forum/ Beijing Normal University, Beijing, China; the financial support of DVK’s travel to the workshop by Recruitment Program of Foreign Experts (RPFE), China (WQ20121100041) is gratefully acknowledged). This study was also presented at the Russian–Finnish Workshop “Endogenous Growth and Sustainable Development” (15-16 November 2013, the Higher School of Economics in St. Petersburg, St. Petersburg, Russia). The authors benefited from fruitful discussions with the participants of both workshops. The research leading to these results has received funding from the European Community’s Seventh Framework Programme under Grant Agreement No. 308601 (COMPLEX). DVK gratefully acknowledges also the financial support from the Russian Foundation for Basic Research (Project No. 12-06-00381).


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