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Note: This package is superseded by GAIO.jl.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.