Order and the ubiquitous occurrence of chaos

A. S. Fokas, T. Bountis

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

For a large class of ODE's, which includes the Van der Pol equation, we determine analytically the asymptotic location of the singularities in the complex t-plane. By integrating these ODE's numerically we show that if the singularities are dense, which is the generic case, the solution is chaotic, in the sense of sensitive dependence on initial conditions. In the exceptional case that the singularities are not dense, the solution exhibits order (taxis). Chaos is ubiquitous even for first order ODE's in complex t.

Original languageEnglish
Pages (from-to)236-244
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Volume228
Issue number1-4
DOIs
Publication statusPublished - Jun 15 1996

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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