Abstract
The concept of Sustainable Development has given rise to multiple interpretations. In this article, it is proposed that Sustainable Development should be interpreted as the capacity of territory, community, or landscape to conserve the notion of well-being that its population has agreed upon. To see the implications of this interpretation, a Brander and Taylor model, to evaluate the implications that extractivist policies have over an isolated community and cooperating communities, is proposed. For an isolated community and through a bifurcation analysis in which the Hopf bifurcation and the heteroclinic cycle bifurcation are detected, 4 prospective scenarios are found, but only one is sustainable under different extraction policies. In the case of cooperation, the exchange between communities is considered by coupling two models such as the one defined for the isolated community, with the condition that their transfers of renewable resources involve conservation policies. Since human decisions do not occur in a continuum, but rather through jumps, the mathematical model of cooperation used is a Filippov System, in which the dynamics could involve two switching manifolds of codimension one and one switching manifold of codimension two. The exchange in the cooperation model, for specific parameter arrangements, exhibits n -periodic orbits and chaos. It is notable that, in the cases in which the system shows sliding, it could be interpreted as a recovery delay related to the time needed by the deficit community to recover, until its dependence on the other community stops. It is concluded (1) that a sustainability analysis depends on the way well-being is defined because every definition of well-being is not necessarily sustainable, (2) that sustainability can be visualized as invariant sets in the nonzero region of the space of states (equilibrium points, n -periodic orbits, and strange attractors), and (3) that exchange is key to the prevalence of the human being in time. The results question us on whether Sustainable Development is only to keep us alive or if it also implies doing it with dignity.
Highlights
Sustainable Development is a concept that has become relevant [1] since due to the series of criticisms that had been made regarding the global model of economic growth, which put the survival of all living species on the planet at risk, including the human being
E global impact of the concept did not lead to a homogeneous school of thought on Sustainable Development, but to the establishment of families of conceptual positions that tried to adapt the concept to their interpretations, as in the case of corporate sustainability and environmental sustainability, which made the word sustainability a suffix or the Latin American case in which the language allowed the differentiation between “sostenible” and “sustentable,” to eradicate the economic character that the concept was taking on political agendas or its interpretations that gave rise to Complexity weak/strong sustainability [3], to sustainable landscapes [4] and to the widely recognized approach of Elkington [5], and the triple bottom line is sustainability from social, economic, and environmental dimensions
E interpretation made in this article of the definition of Sustainable Development proposed by [1]: “satisfying present needs without compromising the satisfaction of the needs of future generations,” assumes (1) that the system of needs is not a unique set, but is defined according to the territory, landscape, or community and the ways of life in them, (2) that the system of needs does not have important changes from one generation to another, (3) that satisfying needs has the purpose of generating well-being, and (4) that this well-being must exist for this generation and any future generation
Summary
Sustainable Development is a concept that has become relevant [1] since due to the series of criticisms that had been made regarding the global model of economic growth, which put the survival of all living species on the planet at risk, including the human being. The purpose of this article is to present the first approach to the study of exchanges between territories, landscapes, and communities within the framework of Sustainable Development from discontinuous piecewise smooth systems and explain the implications of this approach for two communities, based on the analysis of their dynamic behavior Due to it is the first approximation, the mathematical model has variables that define a very simple notion of wellbeing, based on populations and available renewable resources, with which it will seek to demonstrate the conservation of well-being. 2. Effect of the Variation of the Extraction Capacities in a Community e mathematical model on which this article is based is the one developed by Brander and Taylor [78], who presented a general equilibrium model to represent the dynamic interaction between renewable resources and population, seeking to explain the case of Easter Island. Between H and the heteroclinic bifurcation HTC, the population-resources relationship enters into a dynamic of oscillation between scarcity and abundance, which becomes critical when the HTC is exceeded, at which time, followed by a moment at maximum abundance, the population will grow so large that it will critically deplete resources, leading to the collapse of the population and its resources
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