An operational test for distinguishing between complicated and chaotic behavior in deterministic systems

M. Johnson*, J. Habyarimana

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

While various definitions of chaotic processes have been proposed, there is not yet an established operational criterion for computing whether a given process is chaotic. We here use a diffusional measure to characterize whether a given deterministic process and domain is chaotic (operationally defined as exhibiting stochastic behavior). This technique introduces an additional coordinate linked to the process to be examined. By then determining the growth of the second moment of orbit trajectories in this added direction, it can be determined whether the process is chaotic. It is demonstrated that two other commonly used measures of chaos, a positive Lyapunov exponent or the autocorrelation coefficient dropping to zero, fail in certain cases to detect chaotic processes, but this new proposed test works in all the cases examined.

Original languageEnglish (US)
Pages (from-to)289-300
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Volume116
Issue number3-4
DOIs
StatePublished - 1998

Keywords

  • Chaos
  • Diffusion
  • Lyapunov
  • Stochastic

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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