Variable Time Step Dynamics with Choice

Lev Kapitanski, Sanja Živanović Gonzalez

Research output: Contribution to journalArticle

Abstract

We are interested in systems that can and possibly do switch between different regimes; the durations of staying in each regime (dwell times) may vary. We work with the deterministic picture and study global attractors both in the state space and, one of the novelties, in the hyperspace. We give an example of a simple ODE system where the existence or non-existence of attractors depends on the intervals from which the dwell times are chosen. Another novelty is the description of restricted iterated function systems and their attractors. An unexpected corollary is that for the restricted to a subshift hyperbolic IFS, its attractor is the image under Hutchinson’s map (Formula Presented.) of a different, in general, subshift (we call it dual to the original one).

Original languageEnglish (US)
Pages (from-to)745-779
Number of pages35
JournalJournal of Dynamics and Differential Equations
Volume26
Issue number3
DOIs
StatePublished - Nov 4 2014

Fingerprint

Attractor
Dwell Time
Subshift
Hyperspace
Iterated Function System
Global Attractor
Nonexistence
Switch
Corollary
State Space
Vary
Interval

Keywords

  • Iterated functions systems
  • Dwell time
  • Dynamical systems
  • Global attractors
  • Switched systems

ASJC Scopus subject areas

  • Analysis

Cite this

Variable Time Step Dynamics with Choice. / Kapitanski, Lev; Živanović Gonzalez, Sanja.

In: Journal of Dynamics and Differential Equations, Vol. 26, No. 3, 04.11.2014, p. 745-779.

Research output: Contribution to journalArticle

Kapitanski, Lev ; Živanović Gonzalez, Sanja. / Variable Time Step Dynamics with Choice. In: Journal of Dynamics and Differential Equations. 2014 ; Vol. 26, No. 3. pp. 745-779.
@article{b0d1de4bdf714dcc9649f2380c9b2b98,
title = "Variable Time Step Dynamics with Choice",
abstract = "We are interested in systems that can and possibly do switch between different regimes; the durations of staying in each regime (dwell times) may vary. We work with the deterministic picture and study global attractors both in the state space and, one of the novelties, in the hyperspace. We give an example of a simple ODE system where the existence or non-existence of attractors depends on the intervals from which the dwell times are chosen. Another novelty is the description of restricted iterated function systems and their attractors. An unexpected corollary is that for the restricted to a subshift hyperbolic IFS, its attractor is the image under Hutchinson’s map (Formula Presented.) of a different, in general, subshift (we call it dual to the original one).",
keywords = "Iterated functions systems, Dwell time, Dynamical systems, Global attractors, Switched systems",
author = "Lev Kapitanski and {Živanović Gonzalez}, Sanja",
year = "2014",
month = "11",
day = "4",
doi = "10.1007/s10884-014-9374-1",
language = "English (US)",
volume = "26",
pages = "745--779",
journal = "Journal of Dynamics and Differential Equations",
issn = "1040-7294",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Variable Time Step Dynamics with Choice

AU - Kapitanski, Lev

AU - Živanović Gonzalez, Sanja

PY - 2014/11/4

Y1 - 2014/11/4

N2 - We are interested in systems that can and possibly do switch between different regimes; the durations of staying in each regime (dwell times) may vary. We work with the deterministic picture and study global attractors both in the state space and, one of the novelties, in the hyperspace. We give an example of a simple ODE system where the existence or non-existence of attractors depends on the intervals from which the dwell times are chosen. Another novelty is the description of restricted iterated function systems and their attractors. An unexpected corollary is that for the restricted to a subshift hyperbolic IFS, its attractor is the image under Hutchinson’s map (Formula Presented.) of a different, in general, subshift (we call it dual to the original one).

AB - We are interested in systems that can and possibly do switch between different regimes; the durations of staying in each regime (dwell times) may vary. We work with the deterministic picture and study global attractors both in the state space and, one of the novelties, in the hyperspace. We give an example of a simple ODE system where the existence or non-existence of attractors depends on the intervals from which the dwell times are chosen. Another novelty is the description of restricted iterated function systems and their attractors. An unexpected corollary is that for the restricted to a subshift hyperbolic IFS, its attractor is the image under Hutchinson’s map (Formula Presented.) of a different, in general, subshift (we call it dual to the original one).

KW - Iterated functions systems

KW - Dwell time

KW - Dynamical systems

KW - Global attractors

KW - Switched systems

UR - http://www.scopus.com/inward/record.url?scp=84911994815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911994815&partnerID=8YFLogxK

U2 - 10.1007/s10884-014-9374-1

DO - 10.1007/s10884-014-9374-1

M3 - Article

AN - SCOPUS:84911994815

VL - 26

SP - 745

EP - 779

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 3

ER -