EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
expand_more
expand_more
format_list_bulleted
Question
Chapter 10.1, Problem 14E
Interpretation Introduction
Interpretation:
To prove that
Concept Introduction:
➢ Determine the fixed points for the given equation and its stability.
➢ Plot the graph for the equation and compute numerical values.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Page
of 2
ZOOM
+
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 10 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.7 - Prob. 1ECh. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Prob. 7ECh. 10.7 - Prob. 8ECh. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Prob. 11E
Knowledge Booster
Similar questions
- 2. You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1. 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in £ to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 £45 Port 2 £20 £28 Port 3 £13 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form). (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation costs, or can be disposed of at the…arrow_forwardchoose true options in these from given question a) always full and always crossing. b) always full and sometimes crossing. c) always full and never crossing. d) sometimes full and always crossing. e) sometimes full and sometimes crossing. f) sometimes full and never crossing. g) never full and always crossing. h) never full and sometimes crossing. i) never full and never crossing.arrow_forwardAt a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.49. Find the probability that in a sample of 13 customers, at least 7 will order a nonalcoholic beveragearrow_forward
- 10. In the general single period market model with = {W1, W2, W3}, one risky asset, S, and a money market account, we have So = 4 for the risky asset. Moreover, the effective rate of interest on the money market account is 5% and at time t = 1 we have W1 W2 W3 S₁ 100 50 40 21 21 21 (a) Calculate all risk-neutral probability measures for this model. [4 Marks] (b) State if the model is arbitrage-free. Give a brief reason for your answer. [2 Marks] (c) A large bank has designed an investment product with payoff X at time t = 1. Given W₁ W2 W3 X 0 1 1.5 show that X is an attainable contingent claim. [4 marks]arrow_forwardadded 2 imagesarrow_forwardA movie studio wishes to determine the relationship between the revenue generated from the streaming of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Theater revenue, x Streaming revenue, y (in millions of (in millions of dollars) dollars) 13.2 10.3 62.6 10.4 20.8 5.1 36.7 13.3 44.6 7.2 65.9 10.3 49.4 15.7 31.5 4.5 14.6 2.5 26.0 8.8 28.1 11.5 26.1 7.7 28.2 2.8 60.7 16.4 6.7 1.9 Streaming revenue (in millions of dollars) 18+ 16+ 14 12+ xx 10+ 8+ 6+ 2- 0 10 20 30 40 50 60 70 Theater revenue (in millions of dollars) Figure 1 Send data to calculator Send data to Excel The least-squares regression line for these data has a slope…arrow_forward
- help on this, results givenarrow_forwarda) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 x2 x3 81 82 83 84 81 -2 0 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 -2 -2 0 11 0 0-4 0 -8arrow_forwardb) Solve the following linear program using the 2-phase simplex algorithm. You should give the initial tableau, and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. maximize ₁ - 2x2+x34x4 subject to 2x1+x22x3x41, 5x1 + x2-x3-×4 ≤ −1, 2x1+x2-x3-34 2, 1, 2, 3, 40.arrow_forward
- 9. An elementary single period market model contains a risk-free asset with interest rate r = 5% and a risky asset S which has price 30 at time t = 0 and will have either price 10 or 60 at time t = 1. Find a replicating strategy for a contingent claim with payoff h(S₁) = max(20 - S₁, 0) + max(S₁ — 50, 0). Total [8 Marks]arrow_forward8. An elementary single period market model has a risky asset with price So = 20 at the beginning and a money market account with interest rate r = 0.04 compounded only once at the end of the investment period. = = In market model A, S₁ 10 with 15% probability and S₁ 21 with 85% probability. In market model B, S₁ = 25 with 10% probability and S₁ = 30 with 90% probability. For each market model A, B, determine if the model is arbitrage-free. If not, construct an arbitrage. Total [9 Marks]arrow_forwardb) Solve the following linear program using the 2-phase simplex algorithm. You should give the initial tableau, and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. maximize ₁ - 2x2+x34x4 subject to 2x1+x22x3x41, 5x1 + x2-x3-×4 ≤ −1, 2x1+x2-x3-34 2, 1, 2, 3, 40.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning