Working Paper BETA #2017-07

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Title : A simple method to study local bifurcations of three and four-dimensional systems: characterizations and economic applications

Author(s) : Stefano Bosi, David Desmarchelier

Abstract : We provide necessary and sufficient conditions to detect local bifur- cations of three and four-dimensional dynamical systems in continuous time. We characterize not only the bifurcations of codimension one but also those of codimension two. The added value of this methodology rests on its tractability. To illustrate the simplicity of our approach, we provide two analytical applications of dimension three and four to environmental economics, complemented with numerical simulations.

Key-words : local bifurcations, codimensions one and two, pollution, natural capital.

JEL Classification : C61, E32, O44.