Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 11.3, Problem 14E
To determine
The category of the critical points for the plane autonomous system
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(3.3) Find the fixed points of the following dynamical system:
-+v +v, v= 0+v? +1,
and examine their stability.
Question No. 2) Explain the importance of fixed point in discrete dynamical
Systems with the help of two practical examples.
This problem is exercise 5 from Robert L. Devaney's An Introduction to Chaotic Dynamical Systems
Chapter 11 Solutions
Advanced Engineering Mathematics
Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11 - Prob. 1CRCh. 11 - Prob. 2CRCh. 11 - Prob. 3CRCh. 11 - Prob. 4CRCh. 11 - Prob. 5CRCh. 11 - Prob. 6CRCh. 11 - Prob. 7CRCh. 11 - Prob. 8CRCh. 11 - Prob. 11CRCh. 11 - Prob. 12CRCh. 11 - Prob. 13CRCh. 11 - Prob. 15CRCh. 11 - Prob. 16CRCh. 11 - Prob. 17CR
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- Consider the example of injection moulding of a rubber component as shown in Figure Q3(b). The process engineer would like to optimise the strength of the component by optimising the following factors: temperature = 190°C and 210°C, pressure = 50 MPa and 100 MPa, and speed of injection = 10 mm/s and 50 mm/s. What type of mathematical model that the engineer can develop if the relationship is linear and no interactions are significant? Write down the general equation that relates the strength of the component with the process factors.arrow_forwardThis problem is Exercise 3, Section 1.7 from Robert L. Devaney's An Introduction to Chaotic Dynamical Systemsarrow_forwardProblem 5. Find and Classify the critical point of (x,y)=192x³+y²–4xy² on the triangle with vertices (0,0), (4,2) and (-2,2).arrow_forward
- 3. The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 25°C 25°C If the plate is represented by a series of nodes (Fig.1), centered T12 100°C O°C finite-divided differences can substituted for the second T 100°C 0°C derivatives, which results in a system of linear algebraic equations as follows: 75°C 75°C Use the Gauss-Seidel method to solve for the temperatures of the (175 |125 75 25 -1 -1 4 -1 4 nodes in Fig.1. Perform the 0 - 1||T, 2 4 -1|T21 - computation until ɛ, is less than Es = 0.5%. -1 -1 4 [T2 MATH206 week (5) 45 Spring 2021, 20/4/2021arrow_forwardThree components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem. The experiment consists of determining the condition of each component [S (success) for a functioning component and F (failure) for a nonfunctioning component]. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) There us a graph shown in the pictures. Questions are posted on the pictures too.arrow_forwardIn Problems 17–36, use Theorem 2 to find the local extrema.arrow_forward
- 9. discuss the behavior of the dynamical system Xk+1= Axk where -0.31 (@) A = [ (b) A = ["0.3 11 1.5 0.3 (b) A = 0.3 1 3Darrow_forwardProblem 5. Let C be the square oriented counterclockwise with corners (0,0).(7,0).(7,7), and (0,7). If we label the edges of the square as C1, C3, C3, C, starting from the bottom edge going counterclockwise, then the edges may be linearly parameterized, with 0arrow_forwardWhat is the general solution of the following inhomogeneous state space equation?arrow_forwardQuestion 6 [Soalan 6] (C5, CO4, PO2) (a) A causal linear and time-invariant (LTI) discrete system is described by: [Satu sistem diskret kausal liner-masa tidak berubah dijelaskan melalui:] 3 1 2 y(n)- ) — ³ y(n − 1) + 3⁄y(n − 2) = 2x(n) — ²37x(n − 1) - 32 where x(n) and y(n) are the input and the output of the system, respectively. [di mana x(n) dan y(n) masing-masing adalah masukan dan keluaran sistem:] (i) Evaluate the system transfer function, H(z). [Nilaikan rangkap pindah sistem, H(z).] (ii) Evaluate the impulse response, h[n] of the system. [Nilaikan tindak balas dedenyut sistem, h[n].]arrow_forward2. Classify (if possible) each critical point of the given plane autonomous system as a stable node, an unstable node, a stable spiral point, an unstable spiral point or a saddle point. (a) x = x³ - y y = x - y³ (b) x = y - x² + 2 y = 2xy - y (c) x = x (10-x-2y) y=y (16-y - x)arrow_forward3. In M3x2(F), prove that the set { ( ) ( ) ( ) ( ) ( ) } " 0 0 1 is linearly dependent.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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