Conley index for discrete multi-valued dynamical systems

Abstract. We present a numerical method to prove certain statements about the global dynamics of infinitedimensional 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.

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“…By the continuation property of the Conley index, 1)). Finally, the result follows by [12,Theorem 5.4].…”

Section: Robustnessmentioning

confidence: 50%

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

Day¹,

Junge²,

Mischaikow³

2004

SIAM J. Appl. Dyn. Syst.

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“…We have the following basic facts [3,4,6,7,8,9,10]. We shall investigative some properties of I-solution for a dispersive dynamical system f which will be used in the next section.…”

Section: Then F Is Usc If and Only If For Any Open Setmentioning

confidence: 99%

Stable Index Pairs for Dispersive Dynamical Systems

Goo¹,

Park²

2011

Bulletin of the Korean Mathematical Society

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“…Section 3 is devoted to a review from [12] on the basics of modified Morse theory on noncommutative CW complexes. Discrete multivalued dynamical systems have been introduced in [1,9]. In section 4 we develop discrete multivalued dynamical systems on noncommutative CW complexes and provide tools to relate a dynamical picture to the topology and geometry of noncommutative CW complexes.…”

Section: Introductionmentioning

confidence: 99%

Discrete Dynamical System Framework for Construction of Connections between Critical Regions in Lattice Height Data

et al. 2007

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The concept of discrete multivalued dynamical systems for noncommutative CW complexes is developed. Stable and unstable manifolds are introduced and their role in geometric and topological configurations of noncommutative CW complexes is studied. Our technique is illustrated by an example on the noncommutative CW complex decomposition of the algebra of continuous functions on two dimensional torus.2010 MSC: 46L85, 55U10, 54H20, 34D35.

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Conley index for discrete multi-valued dynamical systems

Cited by 62 publications

References 7 publications

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

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

Stable Index Pairs for Dispersive Dynamical Systems

Discrete Dynamical System Framework for Construction of Connections between Critical Regions in Lattice Height Data

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