Dynamic agglomeration patterns in a two-country new economic geography model with four regions. (English) Zbl 1354.91106
Summary: We introduce a two-country New Economic Geography model with four regions. It is defined by a 2D piecewise smooth map that depends on 8 parameters. Using reductions of this map to 1D maps defined on invariant straight lines, we obtain stability conditions of the Core-Periphery fixed points, and show how such reductions can be used to describe basins of attraction of coexisting attractors. Typical bifurcation sequences obtained when varying some parameters are discussed. We find patterns that are much richer than those observed in standard NEG models: there are more types of fixed points including fixed points attracting in Milnor’s sense; their basins of attraction are quite complicated; and coexistence is pervasive.
MSC:
| 91B72 | Spatial models in economics |
| 91D20 | Mathematical geography and demography |
| 37N40 | Dynamical systems in optimization and economics |
| 37M05 | Simulation of dynamical systems |
References:
| [1] | Ago, T.; Isono, I.; Tabuchi, T., Locational disadvantage of the hub, Ann Reg Sci, 40, 819-848 (2006) |
| [2] | Behrens, K.; Gaigné, C.; Ottaviano, G. I.P.; Thisse, J.-F., Countries, regions and trade: on the welfare impacts of economic integration, Eur Econ Rev, 51, 1277-1301 (2007) |
| [3] | Behrens, K., International integration and regional inequalities: how important is national infrastructure?, The Manchester Sch, 79, 5, 952-971 (2011), [ISSN 1467-9957] |
| [4] | Castro, S.; Correia-da-Silva, J.; Mossay, P., The core-periphery model with three regions and more, Pap Reg Sci, 91, 2, 401-418 (2012) |
| [5] | Commendatore, P.; Kubin, I., A three-region new economic geography model in discrete time: preliminary results on global dynamics, (Bischi, G. I.; Chiarella, C.; Sushko, I., Global analysis of dynamic models in economics and finance (2013), Springer-Verlag: Springer-Verlag Berlin), 159-184 · Zbl 1296.91233 |
| [7] | Commendatore, P.; Kubin, I.; Petraglia, C.; Sushko, I., Regional integration, international liberalisation and the dynamics of industrial agglomeration, J Econ Dyn Control, 48, 265-287 (2014) · Zbl 1402.91318 |
| [8] | Commendatore, P.; Kubin, I.; Sushko, I., Typical bifurcation scenario in a three region identical new economic geography model, Math Comput Simul (2014) |
| [9] | Commendatore, P.; Filoso, V.; Kubin, I.; Grafeneder-Weissteiner, T., Towards a multiregional NEG framework: comparing alternative modelling strategies, (Commendatore, P.; Kayam, S. S.; Kubin, I., Complexity and geographical economics: topics and tools (2015), Springer-Verlag: Springer-Verlag Heidelberg) |
| [10] | Krugman, P., Increasing returns and economic geography, J Political Econ, 99, 483-499 (1991) |
| [11] | Krugman, P.; Livas Elizondo, P., Trade policy and the third world metropolis, J Dev Econ, 49, 1, 137-150 (1996) |
| [12] | Paluzie, E., Trade policy and regional inequalities, Pap Reg Sci, 80, 1, 67-85 (2001), [ISSN 1435-5957] |
| [13] | Monfort, P.; Nicolini, R., Regional convergence and international integration, J Urban Econ, 48, 2, 286-306 (2000) |
| [14] | Milnor, J., On the concept of attractor, Commun Math Phys, 99, 177-195, 177-195 (1985) · Zbl 0595.58028 |
| [15] | Mira, C.; Gardini, L.; Barugola, A.; Cathala, J. C., Chaotic dynamics in two-dimensional noninvertible maps (1996), World Scientific: World Scientific Singapore · Zbl 0906.58027 |
| [16] | Wiggins, S., Introduction to applied nonlinear dynamical systems and chaos (2003), Springer-Verlag: Springer-Verlag New York · Zbl 1027.37002 |
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