Models of Continuous Dynamics on the 2-Simplex and Applications in Economics

Stijepic, Denis (2018): Models of Continuous Dynamics on the 2-Simplex and Applications in Economics.

Abstract

In this paper, we discuss the models of continuous dynamics on the 2-simplex that arise when different qualitative restrictions are imposed on the (continuous) functions that generate the dynamics on the 2-simplex. We consider three types of qualitative restrictions: inequality (or set-theoretical) conditions, monotonicity/curvature (or differential-geometrical) conditions, and topological conditions (referring to (transversal) non-(self-)intersection of trajectories). We discuss the implications of these restrictions for transitional and limit dynamics on the 2-simplex and the wide range of potential and existing applications of the resulting system-theoretical models in economics and, in particular, in economic growth and development theory.

• Item Type: MPRA Paper
• Language: English
• Keywords: dynamics; trajectory; 2-simplex; continuous; monotonous; intersection; self-intersection; curvature; Poincaré-Bendixson theory; economics applications
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O11 - Macroeconomic Analyses of Economic Development; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models

References

D. Stijepic, A geometrical approach to structural change modelling, Structural Change and Economic Dynamics 33 (2015) 71–85.

D. Stijepic, Positivistic models of structural change, Journal of Economic Structures 6 (2017a) 1–30.

D. Stijepic, Empirical evidence on the topological properties of structural paths and some notes on its theoretical explanation, MPRA Working Paper No. 82473, 2017b, available online at: https://mpra.ub.uni-muenchen.de/82473/1/MPRA_paper_82473.pdf

W.W. Lee, B.J. Kuipers, Non-intersection of trajectories in qualitative phase space: a global constraint for qualitative simulation, Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI-88), Morgan Kaufmann, Los Altos, CA, 1988.

B. Kuipers, Qualitative simulation, Artificial Intelligence 29 (1986) 289–338.

A.A. Andronov, A.A. Vitt, S.E. Khaikin, Theory of oscillators, Dover Publications, Mineola, New York, 1987.

K. Ciesielski, The Poincaré–Bendixson theorem: from Poincaré to the XXIst century, Central European Journal of Mathematics 10 (2012) 2110–2128.

J. Guckenheimer, P. Holmes, Nonlinear oscillations, dynamical systems, and bifurications of vector fields, Springer, New York, 1990.

J.H. Hale, Ordinary differential equations, Dover Publications, Mineola, New York, 2009.

G. Teschl, Ordinary differential equations and dynamical systems, American Mathematical Society, Providence, Rhode Island, 2012.

D. Stijepic, On the predictability of economic structural change by the Poincaré-Bendixson theory, 2017c, available at SSRN: https://ssrn.com/abstract=3015889.

R. Schettkat, L. Yocarini, The shift to services employment: a review of the literature, Structural Change and Economic Dynamics 17 (2006) 127–147.

J.J. Krüger, Productivity and structural change: a review of the literature, Journal of Economic Surveys 22 (2008) 330–363.

E.G. Silva, A.A.C. Teixeira, Surveying structural change: seminal contributions and a bibliometric account, Structural Change and Economic Dynamics 19 (2008) 273–300.

D. Stijepic, Structural Change and Economic Growth: Analysis within the Partially Balanced Growth- Framework, Südwestdeutscher Verlag für Hochschul- schriften, Saarbruecken, 2011. An older version is available online: http://deposit.fernuni-hagen.de/2763/.

B. Herrendorf, R. Rogerson, Á. Valentinyi, Growth and structural transformation, In: P. Aghion, S.N. Durlauf (Eds.), Handbook of Economic Growth, Volume 2B, Elsevier B.V., Amsterdam, 2014.

L. van Neuss, The drivers of structural change, forthcoming in Journal of Economic Surveys 32 (2018).

D. Stijepic, Empirical evidence on the geometrical properties of structural change trajectories, Research Journal of Economics 1 (2018): 1–10.

D. Stijepic, On development paths minimizing the structural change costs in the three-sector framework and an application to structural policy, 2017d, available at SSRN: https://ssrn.com/abstract=2919806.

D. Stijepic, An argument against Cobb-Douglas production functions (in multi-sector growth modeling), Economics Bulletin 37 (2017e) 1143–1150.