The linearization of a 2-dimensional non-linear system S, is given by J, = 2 The linearization of a second 2-dimensional non-linear system S2 is given by J, = Select all statements that are true about the equilibrium points of these systems based on their linearization. O The equilibrium point of S2 is a saddle point. O The equilibrium point of S1 is a star sink. O The equilibrium point of Si cannot be determined based on its lincarization. O The equilibrium point of S2 cannot be determined based on its linearization. O The equilibrium point of S2 is a center. D The equilibrium point of Si is a saddle point.

The linearization of a 2-dimensional non-linear system S, is given by J, = 2 The linearization of a second 2-dimensional non-linear system S2 is given by J, = Select all statements that are true about the equilibrium points of these systems based on their linearization. O The equilibrium point of S2 is a saddle point. O The equilibrium point of S1 is a star sink. O The equilibrium point of Si cannot be determined based on its lincarization. O The equilibrium point of S2 cannot be determined based on its linearization. O The equilibrium point of S2 is a center. D The equilibrium point of Si is a saddle point.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

10. A factory produces two agricultural pesticides, A and B. For every barrel of A, the factory emits 0.25 kg of carbon monoxide (CO) and 0.60 kg of sulfur dioxide (SO2), and for every barrel of B, it emits 0.50 kg of CO and 0.20 kg of SO2. Pollution laws restrict the factory's output of CO to a maximum of 75 kg and SO2 to a maximum of 90 kg per day. Determine a system of inequalities that describes the number of barrels of each pesticide the factory can produce and still comply the pollution laws.
E9.2 Lotka-Volterra Model. The following Lotka-Volterra equations are a Kolmogorov- type model of predator-prey relationships for interacting populations, e.g. hosts and parasites, yeasts and sugars, sharks and surfers. x₁ = P₁x₁ - P2X1X2 X₁ (0) = x10 x₂ = P3x2 + P1P4X1X2 X₂(0) = x20 (9.11) Parameters p₁ to p4 are constant death and birth rates; x₁ is the host population, x₂ is the par- asite population, and the product x₁x2 represents the "getting-together" of the two species. a) Find the equilibrium steady state solutions for these equations, [xeye]¹ = x₂ in terms of the parameters.
10
Q1. Consider the following characteristic equations. Determine the values of K that corresponds to a stable system. Use the Routh-Hurwitz criterion. (a) s+ 22s + 10s² + 2s + K = 0 (b) s+ 20Ks + 5s²+ (10+K) s+18 = 0 (c) s³ + (K + 0.5) s²+ 4Ks+50 = 0 %3D
Español Assume that traffic flows freely through the intersections A, B, and C. The values x,, x,, and x, and the other numbers in the figure represent flow rates in vehicles per hour. 177 210 196 -- ----- B-- 214 172 121 Part 1 of 7 (a) Write an equation representing equal flow into and out of intersection A. The equation representing equal flow into and out of intersection A is 177 + 196 = x, +x, Part 2 of 7 (b) Write an equation representing equal flow into and out of intersection B. The equation representing equal flow into and out of intersection B is 210 + 214 = x, +x, Part 3 of 7 (c) Write an equation representing equal flow into and out of intersection C. The equation representing equal flow into and out of intersection C is 172 + x, = 121 +x, Part 4 of 7 (a) Write the system of equations from parts (a)-(c) in standard form. The system of equations from parts (a)-(c) in standard form is X1 +X3 = 373 X1+X2 = 424 X2 -X3 = 51 Check Save For Later Submit Assignment
4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;
Explain the determine grren
q12
4
12. (Strang 4.3.1, 5) Consider the four points (t;, b;): (0,0), (1,8), (3, 8), and (4, 20). (a) Set up and solve the system of equations AT Aî = A"b in order to find the best fit line, b = c+ dt. What are the errors for each point relative to the best fit line? (b) Find the best fit horizontal line, b = c; again, set up and solve a system of equations AT Aâ = ATb, but think carefully about what A is. What are the errors for each point relative to this best fit line.
Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(x1, x2) = In ¤1 + In x2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf, y5) = (2a, 2(1 – a)). A type- g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (yi, y) (38, 12(1 – B)). Normalise the price of one unit of berries (good 2) to 1, and let p be the price of one unit of meat (good 1). Which of the following statements is true?