GAIO is a software package for the global numerical analysis of dynamical systems and optimization problems based on set oriented techniques. It may e.g. be used to compute invariant sets, invariant manifolds, invariant measures and almost invariant sets in dynamical systems and to compute the globally optimal solutions of both scalar and multiobjective problems.

References in zbMATH (referenced in 71 articles , 2 standard articles )

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  1. Elamvazhuthi, Karthik; Grover, Piyush: Optimal transport over nonlinear systems via infinitesimal generators on graphs (2018)
  2. Dellnitz, Michael; Klus, Stefan; Ziessler, Adrian: A set-oriented numerical approach for dynamical systems with parameter uncertainty (2017)
  3. Flaßkamp, Kathrin; Ansari, Alex R.; Murphey, Todd D.: Hybrid control for tracking of invariant manifolds (2017)
  4. Junge, Oliver; Kevrekidis, Ioannis G.: On the sighting of unicorns: a variational approach to computing invariant sets in dynamical systems (2017)
  5. Kong, Chen; Liu, Xian-Bin: Noise-induced chaos in a piecewise linear system (2017)
  6. Polotzek, Katja; Padberg-Gehle, Kathrin; Jäger, Tobias: Set-oriented numerical computation of rotation sets (2017)
  7. Denner, Andreas; Junge, Oliver; Matthes, Daniel: Computing coherent sets using the Fokker-Planck equation (2016)
  8. Froyland, Gary; González-Tokman, Cecilia; Watson, Thomas M.: Optimal mixing enhancement by local perturbation (2016)
  9. Hüls, Thorsten: A contour algorithm for computing stable fiber bundles of nonautonomous, noninvertible maps (2016)
  10. Klus, Stefan; Schütte, Christof: Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator (2016)
  11. Schütte, Christof; Koltai, Péter; Klus, Stefan: On the numerical approximation of the Perron-Frobenius and Koopman operator (2016)
  12. Ziessler, Adrian; Hessel-Von Molo, Mirko; Dellnitz, Michael: On the computation of attractors for delay differential equations (2016)
  13. Bittracher, Andreas; Koltai, Péter; Junge, Oliver: Pseudogenerators of spatial transfer operators (2015)
  14. Björnsson, Jóhann; Giesl, Peter; Hafstein, Sigurdur F.; Kellett, Christopher M.: Computation of Lyapunov functions for systems with multiple local attractors (2015)
  15. Hafstein, Sigurdur; Giesl, Peter: Review on computational methods for Lyapunov functions (2015)
  16. Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W.: A data-driven approximation of the koopman operator: extending dynamic mode decomposition (2015)
  17. Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.: Identifying finite-time coherent sets from limited quantities of Lagrangian data (2015)
  18. Baier, R.; Dellnitz, M.; Hessel-von Molo, M.; Sertl, S.; Kevrekidis, I. G.: The computation of convex invariant sets via Newton’s method (2014)
  19. Froyland, Gary; Pollett, Philip K.; Stuart, Robyn M.: A closing scheme for finding almost-invariant sets in open dynamical systems (2014)
  20. Li, Yongqiang; Hou, Zhongsheng: Data-driven asymptotic stabilization for discrete-time nonlinear systems (2014)

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