EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Question
Chapter 5.2, Problem 9E
Interpretation Introduction
Interpretation:
Find characteristic polynomial for system of linear equations,
For the given system of linear equations, the general solution is found.
Classify the fixed points at the origin.
Concept Introduction:
For two dimensional linear system, the equations are
The above linear system is expressed in the form
The standard characteristics polynomials is
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State all the steps.
For the matrix, list the real eigenvalues, repeated according to their multiplicities.
3 -2 0 4
2 1 8
0 3 8
0 0 6
For the matrix, list the real eigenvalues, repeated according to their multiplicities.
Chapter 5 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6E
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- For the system below, find the general solution, sketch the trajectories, being careful to include the eigenvector directions, and classify the type of fixed point: x = y, y = -2(x + y). If the eigenvalues are complex, write the general system in terms of sines and cosines, as above.arrow_forwardEvalute (2xty)dA, wherearrow_forwardFor matrix C, find the associated eigenvalues. c=15₁ 31 C -1 01 and 5 O4 and 3 O-5 and 2 O4 and 6arrow_forward
- For the system below, find the general solution, sketch the trajectories, being careful to include the eigenvector directions, and classify the type of fixed point: 4x - y. x = -x + y, ýarrow_forwardFind two linearly independent solutions of y" + 1xy = 0 of the form Y1 1+ azx³ + a6x® + · ... Y2 = x + b4x4 + b7x + . ... Enter the first few coefficients: Az = -5/6 help (numbers) a6 help (numbers) b4 help (numbers) b7 help (numbers) I| ||arrow_forward
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