Abstract

GRANADA D, H.A.; ANGEL G, M.A.; MORENO O, D.K.  and  CANCHILA M, J.A.. Hopf bifurcation in a model of sustainable development. Ciencia en Desarrollo [online]. 2018, vol.9, n.1, pp.63-70. ISSN 0121-7488.

This article presents a system of three first-orden ordinary differential equations to study the dynamic interaction between renewable resources, population and environmental pollution in a region. The model is achieved coupling a dynamic equation of contamination to formulated systems by Simone D'alessandro and shows that under the Hopf bifurcation can be found conditions to achieve sustainable development under the definition given in the report of Brundtland commission 1987. That is, when a harmonic balance between the state variables of the model is reached.

Keywords : Dynamical systems; nonlinear dynamics; Hopf bifurcation; sustainable development; ecological footprint.

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