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

Hiroyuki Yoshida ()
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Hiroyuki Yoshida: Nihon University

Chapter Chapter 5 in Nonlinearities in Economics, 2021, pp 73-86 from Springer

Abstract: 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.

Keywords: Hopf bifurcation theorem; Lorenz system; Rössler system; Shilnikov theorem; Delay-differential equations (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-030-70982-2_5

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DOI: 10.1007/978-3-030-70982-2_5

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