EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 3.6, Problem 1E
Interpretation Introduction
Interpretation:
To find whether the given diagram is for the parameter
Concept Introduction:
Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.
Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.
Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.
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1) Answer the following questions by circling TRUE or FALSE (No explanation or
work required).
i) If A
=
[1
-2
1]
0 1
6, rank(A) = 3. (TRUE FALSE)
LO
0
0]
ii) If S = {1,x,x², x³} is a basis for P3, dim(P3) = 4 with the standard operations.
(TRUE FALSE)
iii) Let u = (1,1) and v = (1,-1) be two vectors in R². They are orthogonal according
to the following inner product on R²: (u, v) = U₁V₁ + 2U2V2. ( TRUE FALSE)
iv) A set S of vectors in an inner product space V is orthogonal when every pair of
vectors in S is orthogonal. (TRUE FALSE)
v) Dot product of two perpendicular vectors is zero. (TRUE FALSE)
vi) Cross product of two perpendicular vectors is zero. (TRUE FALSE)
2) a) i) Determine which function(s) are solutions of the following linear differential
equation.
-
y (4) — 16y= 0
•
3 cos x
•
3 cos 2x
-2x
•
e
• 3e2x-4 sin 2x
ii) Find the Wronskian for the set of functions that you found from i) as the solution
of the differential equation above.
iii) What does the result…
please help
1. Give a subset that satisfies all the
following properties simultaneously:
Subspace
Convex set
Affine set
Balanced set
Symmetric set
Hyperspace
Hyperplane
2. Give a subset that satisfies some of
the conditions mentioned in (1) but not
all, with examples.
3. Provide a mathematical example
(not just an explanation) of the union of
two balanced sets that is not balanced.
4. What is the precise mathematical
condition for the union of two
hyperspaces to also be a hyperspace?
Provide a proof.
edited 9:11
Chapter 3 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5E
Ch. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.7 - Prob. 1ECh. 3.7 - Prob. 2ECh. 3.7 - Prob. 3ECh. 3.7 - Prob. 4ECh. 3.7 - Prob. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8E
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