Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 6.4, Problem 10E
Interpretation Introduction
Interpretation:
To show that, for
Concept Introduction:
Fixed points of the system are the points where
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(a) Construct a Leslie model with three age classes, so that the intrinsic growth rate is 100%, i. e. the dominant eigenvalue is Lumbda1 = 2 (b) Construct a Leslie model with three age classes, with dominant eigenvalue lumbda1 = 2 and with stable age distribution [0.6 0.3 0.1]^T.
Please step by step answer.
Suppose we are modeling the spread of a disease. People are categorized as either susceptible
or infectious (similar to our Module 7 discussion board). Those who are susceptible do not have the disease,
but could get it. Those who are infected currently have the disease. We assume this disease is not
transmittable by contact with an infectious person. Instead, we will assume it is something that is contracted
through environmental factors.
Define:
dt
= -.035.S
= .03S - .021
where
.
S = number of the people in the population who are susceptible
I= number of the people in the population who are infected
t = time since outbreak observed, days
NOTE: Here we are dealing with the number of people, rather than the proportion of people, in each group.
This fact should not change your analysis in any significant way.
Anyone who is not susceptible or infected falls into a third category: immune. We do not concern ourselves
with this group, because they are people who cannot get the disease…
Which two of the following four values are the eigenvalues of A? Please explain your answer through finding the reduced row echelon form of A, rref(A):
(a) 0
(b) -1
(c) 1
(d) 10
Chapter 6 Solutions
Nonlinear Dynamics and Chaos
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.7 - Prob. 1ECh. 6.7 - Prob. 2ECh. 6.7 - Prob. 3ECh. 6.7 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.8 - Prob. 1ECh. 6.8 - Prob. 2ECh. 6.8 - Prob. 3ECh. 6.8 - Prob. 4ECh. 6.8 - Prob. 5ECh. 6.8 - Prob. 6ECh. 6.8 - Prob. 7ECh. 6.8 - Prob. 8ECh. 6.8 - Prob. 9ECh. 6.8 - Prob. 10ECh. 6.8 - Prob. 11ECh. 6.8 - Prob. 12ECh. 6.8 - Prob. 13ECh. 6.8 - Prob. 14E
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- 2 Let A = -1 and A=-1 is an eigenvalue of A then a= Select one: a. b. 4. C. -2 d.arrow_forwardLet 1 A = -2 1 Consider the system of equations = A. (a) Find all eigenvalues of A. (b) Show that 7 = 0 is the only equilibrium solution of the system. %3D (c) Determine whether 7 Ở is a node, or a saddle, or a spiral point. (d) Determine the stability of 7 = 0. 2.arrow_forwardLet A = ["3 and one of its eigen values is zero, then a = (а) 1 (b) 2 (c) 3 (d) 4arrow_forward
- Find Eiganvalves and semapording eigenvedos of 3 Cx= to %3D 16 Į 3 -1 3arrow_forwardThe eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium (0,0). Is it a stable spiral, an unstable spiral, or a center? A= [ -1 1] [-3 1]arrow_forwardThe Leslie matrix below describes a female cheetah population with four age groups consisting of cubs, adolescents, young adults, and adults, with an initial population that consists of 100 female adults: 0 L= 0 0.06 0 0 0 2.5 3.3 0 0 0 0.7 0 0 0 0.8 0.79] and X (0) = (a) If the largest eigenvalue of L is c = 0.5, what is true about the long-term fate of this population? The population stays the same because the initial population is not an eigenvector The population grows exponentially because the long-term growth rate c is greater than 1 The population grows exponentially because the long-term growth rate c is positive The population dies out because the long-term growth rate c is less than 1 O The population dies out because the initial population is an eigenvector (b) Assume that the general solution for the eigenvectors to the eigenvalue in (a) is given by (3.8z, 0.014z, 0.02z, z) What is the specific eigenvector when z = 20? (c) To compute the proportion of the adolescent females…arrow_forward
- The Leslie matrix below describes a female cheetah population with four age groups consisting of cubs, adolescents, young adults, and adults, with an initial population that consists of 100 female adults: 0 L = 0 0.06 0 0 0 1.7 3.3] 0 0 0 0.7 0 0 0 0.8 0.8 and X (0) = 0 100 (a) If the largest eigenvalue of L is c = 0.62, what is true about the long-term fate of this population? The population grows exponentially because the long-term growth rate c is greater than 1 The population stays the same because the initial population is not an eigenvector The population dies out because the initial population is an eigenvector The population dies out because the long-term growth rate c is less than 1 O The population grows exponentially because the long-term growth rate c is positive (b) Assume that the general solution for the eigenvectors to the eigenvalue in (a) is given by (3.9z, 0.013z, 0.025z, z) What is the specific eigenvector when z = 80? (c) To compute the proportion of the adolescent…arrow_forwardFind the eigenvalue(s) of the linear transformation P2 → P2 given by T(p(x)) = p(-x). A = 1 X = -1arrow_forward(25 %) Q1. For (a) and (b), [A] (a) What are the eigenvalues of A? (b) For each eigenvalue, find a nonzero eigenvector.arrow_forward
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