## Abstract

We present a new way of proving that a computer-generated orbit for the chaotic attractor outside the periodic windows of the quadratic map f_{a} = ax (1 - x) can be shadowed for all time (i-e., there exist true orbits {x_{y}}^{kj-1}_{i=0} which stay near a numerical orbit {p_{i}}^{N}_{i=0} for all time). This is done by computing a numerical orbit for a particular value of a and show that {p_{i}}^{N}_{i=0} ≈ ∪^{m}_{j=1} {x_{ij}}^{kj-1}_{i=0} where Σ^{m}_{j=1} k_{j} = N. The true orbits are found using slightly different maps f_{a}, = a_{j}x(1 - x), where max_{1≤j≤m} (a_{j} - a) < √δ_{p}. This technique can therefore be applied to other chaotic differential equation and discrete systems.

Original language | English (US) |
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Pages (from-to) | 117-129 |

Number of pages | 13 |

Journal | International Journal of Computer Mathematics |

Volume | 70 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1998 |

## Keywords

- Attractors
- Chaotic trajectories
- Quadratic map
- Shadowing

## ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics