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From Local Bifurcations to Global Dynamics: Hopf Systems from the Applied Perspective

In: Nonlinearities in Economics

Author

Listed:
  • Hiroyuki Yoshida

    (Nihon University)

Abstract

This chapter consists of four sections. Section 5.1 reiterates with the Hopf bifurcation theorem. Section 5.2 provides two specific systems that generate chaotic motions by means of numerical simulations. Section 5.3 explains Shilnikov’s theorem. Finally, Sect. 5.4 treats the emergence of chaos in the nonlinear system of the delay-differential equations. To link the chaos theory to economic modelling, at the end of each section, we include simple examples of applications to economics.

Suggested Citation

  • Hiroyuki Yoshida, 2021. "From Local Bifurcations to Global Dynamics: Hopf Systems from the Applied Perspective," Dynamic Modeling and Econometrics in Economics and Finance, in: Giuseppe Orlando & Alexander N. Pisarchik & Ruedi Stoop (ed.), Nonlinearities in Economics, chapter 0, pages 73-86, Springer.
    • Handle: RePEc:spr:dymchp:978-3-030-70982-2_5
    DOI: 10.1007/978-3-030-70982-2_5
    as

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