Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the discrete-time dynamical systems (R, No, S¿) 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(x) = –x. 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.

Consider the discrete-time dynamical systems (R, No, S¿) 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(x) = –x. 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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 16EQ
See similar textbooks
icon
Related questions
Question

This is a Dynamical system question. Please help

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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS