NONLINEAR DYNAMICS AND NON SMOOTH IN A MODEL OF SUSTAINABLE DEVELOPMENT WITH ECONOMIC EXCHANGE BETWEEN TWO SOCIETIES

NONLINEAR DYNAMICS AND NON SMOOTH IN A MODEL OF SUSTAINABLE DEVELOPMENT WITH ECONOMIC EXCHANGE BETWEEN TWO SOCIETIES

Granada, H. A.; Amador, J. A.; Olivar, G.

Full Article:

Mathematical modeling in resources management has been growing in recent years, but this generally describes and studies the dynamic interaction between isolated populations and the ecological complexes to find conditions where human and natural resources coexist in a sustainable scheme. This paper will present a new proposal on two communities that are linked in a scenario of economic exchange, where trading conditions depend on the state variables and parameter values. When several communities are considered and several trading strategies are apply we get rich dynamic and nonlinear phenomena. The analysis concluded that for a sustainable scheme, some parameters must be managed inside the system in order to obtain non-trivial equilibrium or oscillatory behavior between the state variables.

Mathematical modeling in resources management has been growing in recent years, but this generally describes and studies the dynamic interaction between isolated populations and the ecological complexes to find conditions where human and natural resources coexist in a sustainable scheme. This paper will present a new proposal on two communities that are linked in a scenario of economic exchange, where trading conditions depend on the state variables and parameter values. When several communities are considered and several trading strategies are apply we get rich dynamic and nonlinear phenomena. The analysis concluded that for a sustainable scheme, some parameters must be managed inside the system in order to obtain non-trivial equilibrium or oscillatory behavior between the state variables.

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DOI: 10.5151/meceng-wccm2012-19341

Referências bibliográficas

• [1] Brander J. A., TaylorM. S., “The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use”. The American Economics Review. 88, 119-138, 1998.
• [2] Dalton T. R., Coast R.M., “Could institutional reform have saved Easter Island?”. Journal of Evolutionary Economics. 10, 489-505, 2000.
• [3] Reuveny R., Decker C. S., “Easter Island: historical anecdote or warning for the future?”. Ecological Economics. 35, 271-271, 2000.
• [4] D’Alessandro S., “Non-linear dynamics of population and natural resources: The emergence of different patterns of development”. Ecological Economics. 62, 473-481, 2007.
• [5] Kuznetsov, Yuri A., “Elements of Applied Bifurcation Theory”. Springer-Verlang New York., 2004.
• [6] Govaerts, Willy J. F., “Numerical Methods for Bifurcations of Dynamical Equilibria”. SIAM-Philadelphia., 2000.
• [7] Filippov A.F., “Differential equations with discontinuous right-hand sides”. American Mathematical Society Translations. Series 2, AMS, Ann Arbor 199-231, 1964.

Como citar:

Granada, H. A.; Amador, J. A.; Olivar, G.; "NONLINEAR DYNAMICS AND NON SMOOTH IN A MODEL OF SUSTAINABLE DEVELOPMENT WITH ECONOMIC EXCHANGE BETWEEN TWO SOCIETIES", p-3347-3357. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-19341