Homework Answers
Doubt in this then comment below.. i will help you..
.
please thumbs up for this solution..thanks..
.
part c) ....
yes this is possible because (0,0) is stable equillibirum ..so if an initial condition near this point then solution converge to (0,0) ....
Add Answer to:
Task 8. (10+5+5 pt) The following nonlinear system X' = x3 – x, y = x...
Consider the nonlinear system ?x′ = ln(y^2 − x) and y'=x-y-1 (a)Find all the critical points...
Consider the nonlinear system ?x′ = ln(y^2 − x) and y'=x-y-1 (a)Find all the critical points (b)Find the corresponding linearized system near the critical points. (c) Classify the (i) type (node, saddle point, · · · ), and (ii) stability of the critical points for the corresponding linearized system. (d) What conclusion can you obtain for the type and stability of the critical points for the original nonlinear system?
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system...
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system of differential equations dx dt 10x – x2 – 2xy, dy dt 5Y – 3y2 + xy. (a) Determine all of the critical points for the population model. (b) Determine the linearised system for each critical point in part (a) and discuss whether it can be used to approximate the behaviour of the non-linear system. (c) For the critical point at the origin: (i)...
Consider the nonlinear System of differential equations di dt dt (a) Determine all critical points of the system (b) For each critical point with nonnegative x value (20) i. Determine the linearised...
Consider the nonlinear System of differential equations di dt dt (a) Determine all critical points of the system (b) For each critical point with nonnegative x value (20) i. Determine the linearised system and discuss whether it can be used to approximate the ii. For each critical point where the approximation is valid, determine the general solution of iii. Sketch by hand the phase portrait of each linearised system where the approximation behaviour of the non-linear system the linearised system...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the...
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system. 185 Exercises (b) Describe the phase portrait for the nonlinear system (c) Does the linearized system accurately describe the local bchavior near the equilibrium points? (iii) x' = x+ y, y, 2y
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system....
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of th...
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system. 185 Exercises (b) Describe the phase portrait for the nonlinear system (c) Does the linearized system accurately describe the local bchavior near the equilibrium points? x' = sin x, y, = cos y (i)
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated...
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phas...
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 –...
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 – x). (a) Show that the system has a unique fixed point at the origin (0, 0). (b) Use a linear approximation to determine the stability of the fixed point. (c) Apply the Liapunov direct method to determine the stability of the fixed point. Is your conclusion different form that of Part (a)? Why? (d) Can the system have closed orbits (trajectories)? Explain.
Consider the second order equation r" + 2.3-r2-2x = 0. (a) Put y-', and transform the second orde...
Consider the second order equation r" + 2.3-r2-2x = 0. (a) Put y-', and transform the second order equation into an equivalent system of first order equations for (x(t), y(t system Find al critical (equilibrium) points for the (b) For each critical point of the systern from part (a), use linearization to determine the local behaviour (if possible) and stability (if possible) of the critical point. Ski (lı ile 1",lobal phase portrait of the stem frolll pari a Dei ermine...
The following system can be interpreted as a competition system describing the interaction of two species...
The following system can be interpreted as a competition system describing the interaction of two species with populations x(t) and y(t) x' 40x – 22 – ry y' = 30y - y2 – 0.5xy This system has four critical points (0,0), (0, 30), (40,0), and (20, 20). (a) At critical point (20, 20), find the linearization of the system and its eigenvalues. Deter- mine the type and stability of the critical point (20, 20). Base on your work in part...
1. The populations of two competing species x(t) and y(t) are governed by the non-linear system of differential equations dx dt 10x – x2 – 2xy, dy dt 5Y – 3y2 + xy. (a) Determine all of the critical points for the population model. (b) Determine the linearised system for each critical point in part (a) and discuss whether it can be used to approximate the behaviour of the non-linear system. (c) For the critical point at the origin: (i)...
Consider the nonlinear System of differential equations di dt dt (a) Determine all critical points of the system (b) For each critical point with nonnegative x value (20) i. Determine the linearised system and discuss whether it can be used to approximate the ii. For each critical point where the approximation is valid, determine the general solution of iii. Sketch by hand the phase portrait of each linearised system where the approximation behaviour of the non-linear system the linearised system...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system. 185 Exercises (b) Describe the phase portrait for the nonlinear system (c) Does the linearized system accurately describe the local bchavior near the equilibrium points? (iii) x' = x+ y, y, 2y
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system....
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system. 185 Exercises (b) Describe the phase portrait for the nonlinear system (c) Does the linearized system accurately describe the local bchavior near the equilibrium points? x' = sin x, y, = cos y (i)
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated...
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 – x). (a) Show that the system has a unique fixed point at the origin (0, 0). (b) Use a linear approximation to determine the stability of the fixed point. (c) Apply the Liapunov direct method to determine the stability of the fixed point. Is your conclusion different form that of Part (a)? Why? (d) Can the system have closed orbits (trajectories)? Explain.
Consider the second order equation r" + 2.3-r2-2x = 0. (a) Put y-', and transform the second order equation into an equivalent system of first order equations for (x(t), y(t system Find al critical (equilibrium) points for the (b) For each critical point of the systern from part (a), use linearization to determine the local behaviour (if possible) and stability (if possible) of the critical point. Ski (lı ile 1",lobal phase portrait of the stem frolll pari a Dei ermine...
The following system can be interpreted as a competition system describing the interaction of two species with populations x(t) and y(t) x' 40x – 22 – ry y' = 30y - y2 – 0.5xy This system has four critical points (0,0), (0, 30), (40,0), and (20, 20). (a) At critical point (20, 20), find the linearization of the system and its eigenvalues. Deter- mine the type and stability of the critical point (20, 20). Base on your work in part...
Most questions answered within 3 hours.
-
Suppose that Alicia has $30,000 in invested as follows: $10,000
in TJX Cos., $15,000 in Macy’s,...
asked 8 minutes ago -
Volunteer Pharmaceuticals (VP) wants to set aside money in the
R&D fund to seek supplemental drug...
asked 9 minutes ago -
What is precedent?
an order by the court.
the power of a court to overrule a...
asked 15 minutes ago -
Classify the tonicity of a solution made by dissolving 12mg of
sodium chloride in 1.0mL of...
asked 21 minutes ago -
Consider the equilibrium reaction: 2A (aq) + 3B (aq) <-->
C (aq) (in my notation <-->...
asked 22 minutes ago -
A recent poll found that 21% of a random sample of 1200 people
lost jobs due...
asked 28 minutes ago -
Indicate whether aqueous solutions of the following substances
contain ions. If so, write formulas for the...
asked 23 minutes ago -
Include at least one psychology theory, model or concept
discussed in Chapter 1, 2 or the...
asked 33 minutes ago -
Need help in drawing out a map pathway of pentose phosphate
pathway and pyruvate dehydrogenase/citric acid...
asked 40 minutes ago -
Question 1
At the end of Year 6,
South Co.'s tax department estimates that they will...
asked 42 minutes ago -
Use standard enthalpies of formation to determine
ΔHorxn for:
1. 3NO2(g) + H2O(l) → 2HNO3(aq)
+...
asked 46 minutes ago -
Abigail Adams was hired as an associate professor of economics
at Heartland University. She was the...
asked 49 minutes ago