Local bifurcations of three and four-dimensional systems: A tractable characterization with economic applications

We provide necessary and sufficient conditions to detect local bifurcations 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. For the sake of completeness, we give also the non-degeneracy conditions for each bifurcation. The added value of our methodology rests on its generality. To illustrate the tractability of our approach, we provide two analytical applications of dimension three and four to environmental economics, complemented with numerical simulations. (C) 2018 Elsevier B.V. All rights reserved.