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attractivity (attracts points in a neighbourhood W of I, attracts points in R, attracts all compact sets in R, attracts all sets in R) and stability (unstable, stable, asymptotically stable, globally asymptotically stable) (a) f(x) = 0. Determine the (only) compact and invariant set I. (b) f(x) = -x. Show that I = and stability. Is {0} the only compact and invariant set? Prove your answer. {0} is a compact and invariant set, and determine its attractivity

attractivity (attracts points in a neighbourhood W of I, attracts points in R, attracts all compact sets in R, attracts all sets in R) and stability (unstable, stable, asymptotically stable, globally asymptotically stable) (a) f(x) = 0. Determine the (only) compact and invariant set I. (b) f(x) = -x. Show that I = and stability. Is {0} the only compact and invariant set? Prove your answer. {0} is a compact and invariant set, and determine its attractivity

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Need help with discrete-time dynamical system problem about stability and attractivity.

Consider the discrete-time dynamical systems (R, No, St) given by the iteration of the map f:R → R below. Determine and prove the attractivity and stability properties of I, using the definition: • attractivity (attracts points in a neighbourhood W of I, attracts points in R, attracts all compact sets in R, attracts all sets in R) • and stability (unstable, stable, asymptotically stable, globally asymptotically stable) (a) f(x) = 0. Determine the (only) compact and invariant set I. (b) f(г) — —г. = -: Show that I {0} is a compact and invariant set, and determine its attractivity and stability. Is {0} the only compact and invariant set? Prove your answer.
Transcribed Image Text:Consider the discrete-time dynamical systems (R, No, St) given by the iteration of the map f:R → R below. Determine and prove the attractivity and stability properties of I, using the definition: • attractivity (attracts points in a neighbourhood W of I, attracts points in R, attracts all compact sets in R, attracts all sets in R) • and stability (unstable, stable, asymptotically stable, globally asymptotically stable) (a) f(x) = 0. Determine the (only) compact and invariant set I. (b) f(г) — —г. = -: Show that I {0} is a compact and invariant set, and determine its attractivity and stability. Is {0} the only compact and invariant set? Prove your answer.
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