Periodic solutions and global indeterminacy in a model of sustainable tourism

Year 2017, Volume: 3 Issue: 2, 89 - 97, 01.07.2017

Giovanni Bella

https://doi.org/10.24288/jttr.314591

Abstract

The impact of
tourism on economic growth and environmental degradation is one of the most
relevant debated issues. Despite the huge strand of empirical literature on the
topic, a formalized theoretical investigation of the link between tourism and
sustainable economic growth is unfortunately still lacking. To this end, and in
line with the literature on the tourist life-cycle hypothesis, we present an endogenous
growth model to study the impact of tourism activities and natural resource use
on the long run steady state. The aim is to use the principles of bifurcation
theory to gain hints on the global properties of the equilibrium, and show the
existence of irregular patterns, either indeterminate or chaotic, which
possibly suggest the emergence of a (low growth) poverty-environment trapping
region.

Keywords

Sustainable tourism, Complex dynamics, Economic growth, Poverty trap

References

• Algaba, A., Freire, E., & Gamero, E. (1999). Hypernormal forms for equilibria of vector fields. Codimension one linear degeneracies. Rocky Mountain Journal of Mathematics, 29, 13-45.
• Baggio, R. (2008). Symptoms of complexity in a tourism system. Tourism Analysis, 13(1), 1-20.
• Bella, G., & Mattana, P. (2014). Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov-Takens bifurcation. Mathematical Social Sciences, 71, 69-79.
• Benhabib, J., Schmitt-Grohé, S., & Uribe, M. (2001). The perils of Taylor rules. Journal of Economic Theory, 96, 40-69.
• Bornhorst, T., Ritchie, J., & Sheehan, L. (2010). Determinants of Tourism Success for DMOs & destinations: An Empirical Examination of Stakeholders' Perspectives. Tourism Management, 31, 572-589.
• Brau, R., Lanza, A., & Pigliaru, F. (2007). How fast are small tourism countries growing? Evidence from the data for 1980-2003. Tourism Economics, 13(4), 603-613.
• Brida, J. G., Sanchez Carrera, E. J., & Risso, W. A. (2008). Tourism's Impact on Long-Run Mexican Economic Growth. Economics Bulletin, 3(21), 1-8.
• Butler, R. (1980). The concept of a tourist area cycle of evolution. Canadian Geographer, 24, 5-12.
• Cole, S. (2009). A logistic tourism model: Resort Cycles, Globalization and Chaos. Annals of Tourism Research, 36(4), 689-714.
• Finco, M. V. A. (2009). Poverty-Environment Trap: A non linear probit model applied to rural areas in the North of Brazil. American-Eurasian J. Agric. & Environ. Sci., 5(4), 533-539.
• Gamero, E., Freire, E., & Ponce, E. (1991). Normal forms for planar systems with nilpotent linear part. In R. Seydel, F. W. Schneider, T. Küpper, & H. Troger (Eds.), Bifurcation and Chaos: Analysis,
• Algorithms, Applications. International Series of Numerical Mathematics, (pp. 123-12). Basel, Birkhäuser.
• Katircioglu, S. T. (2009). Testing the tourism-led growth hypothesis: The case of Malta. Acta Oeconomica, 59(3), 331-343.
• Mattana, P., & Venturi, B. (1999). Existence and stability of periodic solutions in the dynamics of endogenous growth. International Review of Economics and Business, 46, 259-284.
• Musu, I. (1995). Transitional Dynamics to Optimal Sustainable Growth. FEEM Working Paper 50.95.
• Nowak, J. J., Sahli, M., & Cortés-Jiménez, I. (2007). Tourism, capital good imports and economic growth: theory and evidence for Spain. Tourism Economics, 13(4), 515-536.
• Rosendahl, K. E. (1996). Does improved environmental policy enhance economic growth?. Environmental and Resource Economics, 9, 341-364.
• Sachs, J. D., & Warner, A. M. (2001). Natural resources and economic development: The curse of natural resources. European Economic Review, 45, 827-838.
• Schubert, F. S., Brida, J. G., & Risso, W. A. (2010). The impacts of international Tourism demand on economic growth of small economies dependent of tourism. Tourism Management, 32(2), 377-385.
• Shang, D., & Han, M. (2005). The existence of homoclinic orbits to saddle-focus. Applied Mathematics and Computation, 163, 621-631.
• Shilnikov, L. P. (1965). A case of the existence of a denumerate set of periodic motions. Sov. Math. Docl., 6, 163-166.