### 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 language | English (US) |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 147-185 |

Number of pages | 39 |

DOIs | |

State | Published - Jan 1 2011 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 173 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*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

**Fractal Basin Boundaries.** / Lai, Ying-Cheng; Tél, Tamás.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Applied Mathematical Sciences (Switzerland).*Applied Mathematical Sciences (Switzerland), vol. 173, Springer, pp. 147-185. https://doi.org/10.1007/978-1-4419-6987-3_5

}

TY - CHAP

T1 - Fractal Basin Boundaries

AU - Lai, Ying-Cheng

AU - Tél, Tamás

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - Chaotic Attractor

KW - Invariant Subspace

KW - Lyapunov Exponent

KW - Stable Manifold

KW - Unstable Manifold

UR - http://www.scopus.com/inward/record.url?scp=84978897959&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978897959&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-6987-3_5

DO - 10.1007/978-1-4419-6987-3_5

M3 - Chapter

AN - SCOPUS:84978897959

T3 - Applied Mathematical Sciences (Switzerland)

SP - 147

EP - 185

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -