Noninvertibility and the structure of basins of attraction in a model adaptive control system

Raymond A. Adomaitis, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

We present a two-dimensional, nonlinear map, arising from a simple adaptive control problem, which exhibits disconnected boundaries separating the basins of attraction of its coexisting attractors. We perform a detailed study of the relation between this phenomenon and the noninvertible nature of the map and demonstrate how the complex basin structure is caused by a change in the number of preimages of points along a stable manifold.

Original languageEnglish (US)
Pages (from-to)95-105
Number of pages11
JournalJournal of Nonlinear Science
Volume1
Issue number1
DOIs
StatePublished - Feb 1 1991

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Applied Mathematics
  • Mathematics(all)
  • Mechanics of Materials
  • Computational Mechanics

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