Order and the ubiquitous occurrence of chaos

A. S. Fokas, T. Bountis

Research output: Contribution to journalArticle

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
Externally publishedYes

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chaos
Chaos
occurrences
Singularity
Van Der Pol Equation
Initial conditions
First-order
Class

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Order and the ubiquitous occurrence of chaos. / Fokas, A. S.; Bountis, T.

In: Physica A: Statistical Mechanics and its Applications, Vol. 228, No. 1-4, 15.06.1996, p. 236-244.

Research output: Contribution to journalArticle

Fokas, A. S. ; Bountis, T. / Order and the ubiquitous occurrence of chaos. In: Physica A: Statistical Mechanics and its Applications. 1996 ; Vol. 228, No. 1-4. pp. 236-244.
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