A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems | Zendy

Sarah Day | Zendy; Oliver Junge | Zendy; Konstantin Mischaikow | Zendy

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A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems

Author(s) -

Sarah Day,

Oliver Junge,

Konstantin Mischaikow

Publication year - 2004

Publication title -

siam journal on applied dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.218

H-Index - 61

ISSN - 1536-0040

DOI - 10.1137/030600210

Subject(s) - computation , dynamical systems theory , invariant (physics) , chaotic , mathematics , phase space , numerical analysis , set (abstract data type) , computer science , statistical physics , mathematical analysis , algorithm , physics , quantum mechanics , artificial intelligence , mathematical physics , thermodynamics , programming language

We present a numerical method to prove certain statements about the global dy- namics of infinite dimensional maps. The method combines set-oriented numerical tools for the computation of invariant sets and isolating neighborhoods, the Conley index theory and analytic considerations. It not only allows for the detection of a certain dynamical behaviour, but also for a precise computation of the corresponding invariant sets in phase space. As an example computation we show the existence of period points, connecting orbits and chaotic dynamics in the Kot-Schaer growth-dispersal model for plants.

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