
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 12.4, Problem 1E
Interpretation Introduction
Interpretation:
To prove time delay trajectory for the following figure traces an ellipse for 0<τ<π2
Concept Introduction:
The general format of the ellipse equation is
Ax2+ Bxy + Cy2+ Dx + Ey + F = 0
A, B, C, D, E, F are constants and (x,y) is a set of points.
The condition for non-degenerate real ellipse is,
B2−4AC<0 and
C|AB2D2B2CE2D2E2F|=CΔ<0
If CΔ>0, ellipse is imaginary, and if Δ=0, then ellipse is a point.
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LARLINALG8 7.4.003.
Use the age transition matrix L and age distribution vector X1 to find the age distribution vectors X2 and x3.
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Then find a stable age distribution vector.
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Use the age transition matrix L and age distribution vector X1 to find the age distribution vectors x2 and ×3.
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LARLINALG8 7.3.003.
Prove that the symmetric matrix is diagonalizable. (Assume that a is real.)
0 0 a
A =
a 0
a 0 0
Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list the same eigenvalue multiple times.)
λ=
Find an invertible matrix P such that P-1AP is diagonal.
P =
Which of the following statements is true? (Select all that apply.)
☐ A is diagonalizable because it is a square matrix.
A is diagonalizable because it has a determinant of 0.
A is diagonalizable because it is an anti-diagonal matrix.
A is diagonalizable because it has 3 distinct eigenvalues.
A is diagonalizable because it has a nonzero determinant.
A is diagonalizable because it is a symmetric…
Use the method of undetermined coefficients to solve the given nonhomogeneous system.
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Chapter 12 Solutions
Nonlinear Dynamics and Chaos
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.2 - Prob. 1E
Ch. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5E
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