Fractal Basin Boundaries

Ying-Cheng Lai, Tamás Tél

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations

Abstract

Dissipative dynamical systems often possess multiple coexisting attractors. The set of initial conditions leading to trajectories landing on an attractor is the basin of attraction of this attractor. Each attractor thus has its own basin, which is invariant under the dynamics, since images of every point in the basin still belong to the same basin. The basins of attraction are separated by boundaries. We shall demonstrate that it is common for nonlinear systems to have fractal basin boundaries, the dynamical reason for which is nothing but transient chaos on the boundaries. In fact, fractal basin boundaries contain one or several nonattracting chaotic sets.

Original languageEnglish (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages147-185
Number of pages39
DOIs
StatePublished - Jan 1 2011

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume173
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

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Keywords

  • Chaotic Attractor
  • Invariant Subspace
  • Lyapunov Exponent
  • Stable Manifold
  • Unstable Manifold

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Lai, Y-C., & Tél, T. (2011). Fractal Basin Boundaries. In Applied Mathematical Sciences (Switzerland) (pp. 147-185). (Applied Mathematical Sciences (Switzerland); Vol. 173). Springer. https://doi.org/10.1007/978-1-4419-6987-3_5