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gaio

Matlab toolbox for set-oriented numerics in dynamical systems

https://github.com/gaioguy/gaio

Science Score: 31.0%

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Repository

Matlab toolbox for set-oriented numerics in dynamical systems

Basic Info
  • Host: GitHub
  • Owner: gaioguy
  • Language: C
  • Default Branch: master
  • Homepage:
  • Size: 2.05 MB
Statistics
  • Stars: 18
  • Watchers: 6
  • Forks: 8
  • Open Issues: 1
  • Releases: 1
Created over 10 years ago · Last pushed about 2 years ago
Metadata Files
Readme License Citation

README.md

GAIO

(Global Analysis of Invariant Objects) is a Matlab toolbox for the computational analysis of dynamical systems. It provides data structures and algorithms for the set-oriented computation of * invariant sets (maximal invariant set, chain recurrent set, periodic points, global attractor) of arbitrary dimension or topology * invariant manifolds (stable/unstable manifold of an arbitrary invariant set) * invariant measures, almost invariant sets, coherent sets * value functions for optimal control problems

Note: This package is superseded by GAIO.jl.

Installation

After unpacking the archive add the resulting folder to your Matlab path, e.g.

>> addpath(genpath('/Users/gaioguy/GAIO'))

Note: Compatibility with Octave is currently untested.

Documentation

References

  • Dellnitz, M.; Froyland, G.; Junge, O.: The algorithms behind GAIO - Set oriented numerical methods for dynamical systems, in: B. Fiedler (ed.): Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, 2001.
  • Dellnitz, M.; Junge, O.: On the approximation of complicated dynamical behavior, SIAM Journal on Numerical Analysis, 36 (2), 1999.
  • Dellnitz, M.; Hohmann, A.: A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik 75, pp. 293-317, 1997.

Owner

  • Name: Oliver Junge
  • Login: gaioguy
  • Kind: user
  • Location: Munich, Germany
  • Company: Technische Universität München

Citation (CITATION-2.cff) 

# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!

cff-version: 1.2.0
title: GAIO
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: Oliver
    family-names: Junge
repository-code: 'https://github.com/gaioguy/GAIO'
abstract: >-
  GAIO (Global Analysis of Invariant Objects) is a C library
  and Matlab toolbox for the computational analysis of
  dynamical systems. GAIO provides data structures and
  algorithms for the approximation of invariant sets
  (maximal invariant set, chain recurrent set, attractor) of
  arbitrary dimension or topology, invariant manifolds
  (stable/unstable manifold of an arbitrary invariant set).
  Based on these, Galerkin discretizations of the
  Frobenius-Perron and the Koopman operator are provided,
  enabling the approximation of invariant measures, almost
  invariant sets, almost cyclic as well as coherent sets.
keywords:
  - >-
    dynamical system, set-oriented numerics, box
    discretization, transfer operator, Koopman operator,
    invariant set, invariant measure
version: '3.0'
date-released: '2015-12-31'

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