Topological entropy of composition and impulsive differential equations satisfying a uniqueness condition

Jan Andres and Pavel Ludvík

Chaos, Solitons & Fractals, 2022, vol. 156, issue C

Abstract: The impulsive differential equations are examined via the associated Poincaré translation operators in terms of topological entropy. The crucial role is played by the entropy analysis of the compositions of Poincaré’s operators with the impulsive maps. For the scalar (one-dimensional) problems, the lower entropy estimations can be effectively obtained by means of horseshoes. For the vector (higher-dimensional) problems, the situation becomes more delicate and requires rather sophisticated techniques. Five main theorems are presented about a positive topological entropy (i.e. topological chaos) for given impulsive problems. For vector linear homogeneous differential equations with constant coefficients and isometric impulses, the zero entropy is deduced under commutativity restrictions imposed on the components of a mentioned composition. Several illustrative examples and numerical simulations are supplied.

Keywords: Topological entropy; Impulsive differential equations; Entropy of composition; Poincaré operators; Horseshoes; Topological chaos (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007792200011X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:156:y:2022:i:c:s096007792200011x

DOI: 10.1016/j.chaos.2022.111800

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().