Coupled chaotic fluctuations in a model of international trade and innovation: Some preliminary results

Iryna Sushko*, Laura Gardini, Kiminori Matsuyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider a two-dimensional continuous noninvertible piecewise smooth map, which characterizes the dynamics of innovation activities in the two-country model of trade and product innovation proposed in [7]. This two-dimensional map can be viewed as a coupling of two one-dimensional skew tent maps, each of which characterizes the innovation dynamics in each country in the absence of trade, and the coupling parameter depends inversely on the trade cost between the two countries. Hence, this model offers a laboratory for studying how a decline in the trade cost, or globalization, might synchronize endogenous fluctuations of innovation activities in the two countries. In this paper, we focus on the bifurcation scenarios, how the phase portrait of the two-dimensional map changes with a gradual decline of the trade cost, leading to border collision, merging, expansion and final bifurcations of the coexisting chaotic attractors. An example of peculiar border collision bifurcation leading to an increase of dimension of the chaotic attractor is also presented.

Original languageEnglish (US)
Pages (from-to)287-302
Number of pages16
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume58
DOIs
StatePublished - May 2018

Keywords

  • A two-country model of trade and product innovation
  • Bifurcation scenarios
  • Border collision bifurcation
  • Skew tent map
  • Two-dimensional noninvertible piecewise smooth map

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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