A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. (English) Zbl 1059.37068

Day, S.; Junge, O.; Mischaikow, K.

SIAM J. Appl. Dyn. Syst. 3, No. 2, 117-160 (2004).

Summary: We present a numerical method to prove certain statements about the global dynamics 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 behavior, 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-Schaffer growth-dispersal model for plants.

MSC:

37M99	Approximation methods and numerical treatment of dynamical systems
37B10	Symbolic dynamics
37B30	Index theory for dynamical systems, Morse-Conley indices
37C70	Attractors and repellers of smooth dynamical systems and their topological structure
65Q05	Numerical methods for functional equations (MSC2000)
37N35	Dynamical systems in control

Keywords:

Conley index; numercial method; infinite-dimensional maps; Kot-Schaffer model for plants; invariant sets

Software:

GAIO; b4m