Local bifurcations of three and four-dimensional systems : A tractable characterization with economic applications
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- handle: 10670/1.oc2kpr
- hal: hal-02512900
- doi: 10.1016/j.mathsocsci.2018.11.001
- PRODINRA: 466630
- WOS: 000459519500005
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Mots-clés
Local bifurcations Codimensions one and two Pollution Natural capital C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C61 - Optimization Techniques • Programming Models • Dynamic Analysis E - Macroeconomics and Monetary Economics/E.E3 - Prices, Business Fluctuations, and Cycles/E.E3.E32 - Business Fluctuations • Cycles O - Economic Development, Innovation, Technological Change, and Growth/O.O4 - Economic Growth and Aggregate Productivity/O.O4.O44 - Environment and GrowthSujets proches
Economic growth Growth, Economic Development, Economic TradeCiter ce document
Stefano Bosi et al., « Local bifurcations of three and four-dimensional systems : A tractable characterization with economic applications », HAL-SHS : économie et finance, ID : 10.1016/j.mathsocsci.2018.11.001
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Résumé
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.