EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
Question
Book Icon
Chapter 5.1, Problem 10E
Interpretation Introduction

Interpretation:

To determine whether the origins of the given systems of differential equations are attracting, Liapunov stable, asymptotically stable or none of these.

Concept Introduction:

Point x* of a system x˙ = f(x) is attracting, if any trajectory that starts within a distance δ of x* isguaranteed to converge to x* eventually.

I.e. x* is attracting, if there is a δ> 0, such that limtx(t) = x*, whenever x(0) - x* < δ.

Point is Liapunov stable, if nearby trajectories remain close for alltime.

I.e. for each ε> 0, there is a δ> 0, such that x(0) - x* < ε, whenever x(0) - x* < δ.

x* isasymptotically stable, if it is both attracting and Liapunov stable.

Blurred answer
Students have asked these similar questions
(b) Let I[y] be a functional of y(x) defined by [[y] = √(x²y' + 2xyy' + 2xy + y²) dr, subject to boundary conditions y(0) = 0, y(1) = 1. State the Euler-Lagrange equation for finding extreme values of I [y] for this prob- lem. Explain why the function y(x) = x is an extremal, and for this function, show that I = 2. Without doing further calculations, give the values of I for the functions y(x) = x² and y(x) = x³.
Please use mathematical induction to prove this
L sin 2x (1+ cos 3x) dx 59
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Text book image
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Text book image
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Text book image
Basic Technical Mathematics
Advanced Math
ISBN:9780134437705
Author:Washington
Publisher:PEARSON
Text book image
Topology
Advanced Math
ISBN:9780134689517
Author:Munkres, James R.
Publisher:Pearson,