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Planar Non-Linear ODE: The Regular Case

In: Economic Dynamics and Distributions

Author

Listed:
  • Paulo B. Brito

    (University of Lisbon, Lisbon School of Economics and Management)

Abstract

The material of the previous two chapters allows us to shortly present some of the main elements of the qualitative theory of regular non-linear ordinary differential equations. This chapter studies several normal forms for planar systems, highlighting the main differences between local and global dynamics, between generic and non-generic dynamic phenomena—as heteroclinic, and homoclinic orbits, and limit cycles—and the associated (regular) bifurcations. It also presents applications on economics, in particular, to the benchmark Ramsey model, the possible dynamics of maximized Hamiltonian dynamic systems, and the difference between bifurcation and comparative dynamics analyses.

Suggested Citation

  • Paulo B. Brito, 2026. "Planar Non-Linear ODE: The Regular Case," Dynamic Modeling and Econometrics in Economics and Finance, in: Economic Dynamics and Distributions, chapter 0, pages 137-170, Springer.
    • Handle: RePEc:spr:dymchp:978-3-031-94717-9_5
    DOI: 10.1007/978-3-031-94717-9_5
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