EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 9.3, Problem 8E
Interpretation Introduction

Interpretation:

To find if D is an invariant set, if D is considered to be the disk x2 + y21, for the system in polar coordinates given by r˙ = r(1 - r2), θ˙ = 1. To find if D attracts an open set of initial conditions. To find if D an attractor; if yes, to find its basin of attraction. To find if the circle x2 + y2=1 is an attractor; if yes, to find its basin of attraction.

Concept Introduction:

  • ➢ An attractor is a closed set A such that with the following properties:

    Any trajectory that starts in A stays in A for all time.

    A attracts an open set of initial conditions.

    There is no proper subset of A that fulfills the above two conditions.

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Students have asked these similar questions
Question 1. Prove that the function f(x) = 2; f: (2,3] → R, is not uniformly continuous on (2,3].
Consider the cones K = = {(x1, x2, x3) | € R³ : X3 ≥√√√2x² + 3x² M = = {(21,22,23) (x1, x2, x3) Є R³: x3 > + 2 3 Prove that M = K*. Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix A.
I am unable to solve part b.
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