Homework Answers
![9) ☆ led na of (ay) yla gay? 3 (w?y)= 15:] [ an (40-20-4 -0.5 30-2y-0.54 3 3(20,20)- -20 -20 -20 -10 Linerization =) nz-20](http://img.homeworklib.com/questions/7a85e380-e7cf-11ea-b53d-d1d88976f921.png?x-oss-process=image/resize,w_560)
Add Answer to:
The following system can be interpreted as a competition system describing the interaction of two species...
The following problem can be interpreted as describing the interaction of two species with populations x...
The following problem can be interpreted as describing the interaction of two species with populations x and y. (A computer algebra system is recommended.) dx dy =y(3.5-y-s). (b) Find the critical points. (Order your answers from smallest to largest x, then from smallest to largest y.) G1 (x, ) 0,0 C2 (x, y)-(10. C3 (x, y) (11,0 (c) For each critical point find the corresponding linear system. (Let u =x-xo and v = y-yo where (Xo, yo) is the critical...
Q1. The following nonlinear system of DE's can be interpreted as describing the inter- action of ...
please give specific steps of
all the questions, thanks
Q1. The following nonlinear system of DE's can be interpreted as describing the inter- action of two species with population densities r and y, respectively. 1dy1 2dt 2 dt (a) Write the given system in the form where A is a matrix with constant enteries. Also, show that the system is locally linear. (b) This system has three equilibrium or critical points. Determine those critical points and give a physical interpretation...
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 plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the syst...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
1 Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b)...
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
a) Interaction between two interaction between the species is described by the following system. (A) fixed points. Assume 0 and y 2 0. (only 1st qundrant) species. Let r and y represent the popul...
a) Interaction between two interaction between the species is described by the following system. (A) fixed points. Assume 0 and y 2 0. (only 1st qundrant) species. Let r and y represent the populations of two species. The assify the Find and el (B) Sketch the phase portrait. Show only the 1st quadrant. Include nullelines. (C) Interpret your results in terms of the two species.
a) Interaction between two interaction between the species is described by the following system. (A)...
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...
Problem 1 (20 points) Given the following non-linear autonomous system, || x' = 2cy " ||...
Problem 1 (20 points) Given the following non-linear autonomous system, || x' = 2cy " || y' = 9-+ y2 : a) What are the equilibrium points? (2 points) b) Can you tell their stability via linearization? If you can, please determine their stability and if they are locally a sink, a port or a source. If you cannot, please explain why. (3 points) c) Please find a first integral of the form f (2,y) = xg (22 + y2)...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and =...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
The following problem can be interpreted as describing the interaction of two species with populations x and y. (A computer algebra system is recommended.) dx dy =y(3.5-y-s). (b) Find the critical points. (Order your answers from smallest to largest x, then from smallest to largest y.) G1 (x, ) 0,0 C2 (x, y)-(10. C3 (x, y) (11,0 (c) For each critical point find the corresponding linear system. (Let u =x-xo and v = y-yo where (Xo, yo) is the critical...
please give specific steps of
all the questions, thanks
Q1. The following nonlinear system of DE's can be interpreted as describing the inter- action of two species with population densities r and y, respectively. 1dy1 2dt 2 dt (a) Write the given system in the form where A is a matrix with constant enteries. Also, show that the system is locally linear. (b) This system has three equilibrium or critical points. Determine those critical points and give a physical interpretation...
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 plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
a) Interaction between two interaction between the species is described by the following system. (A) fixed points. Assume 0 and y 2 0. (only 1st qundrant) species. Let r and y represent the populations of two species. The assify the Find and el (B) Sketch the phase portrait. Show only the 1st quadrant. Include nullelines. (C) Interpret your results in terms of the two species.
a) Interaction between two interaction between the species is described by the following system. (A)...
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...
Problem 1 (20 points) Given the following non-linear autonomous system, || x' = 2cy " || y' = 9-+ y2 : a) What are the equilibrium points? (2 points) b) Can you tell their stability via linearization? If you can, please determine their stability and if they are locally a sink, a port or a source. If you cannot, please explain why. (3 points) c) Please find a first integral of the form f (2,y) = xg (22 + y2)...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and =...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
Most questions answered within 3 hours.
-
Using the OSHA web site find the OSHA regulation for personal eye
protection. Write a summary...
asked 29 seconds ago -
In 600 words, answer the following
1) Why has the transfer of defense technologies to domestic...
asked 30 seconds ago -
One difference between periodic and perpetual inventory systems
is:
Multiple Choice Cost of goods sold is...
asked 1 minute ago -
Balance the following oxidation-reduction equations using redox
methods:
Cu + H+ --------> Cu+ +
H2
asked 21 minutes ago -
For a voltaic cell based on the reaction below, which statement
is correct?
Zn(s)+2H+(aq)→Zn2+(aq)+H2(g)
Zn2+(aq) is...
asked 4 minutes ago -
For the balanced reaction: CaCl2 (aq) + Na2CO3 (aq) -> CaCO3
(s) + 2 NaCl (aq),...
asked 15 minutes ago -
1. If ln(x)=ln(x)= -0.2 , what does xx equal? Round
your answer to three significant figures. The...
asked 11 minutes ago -
what is the current research being done on the hexokinase
enzyme?
asked 17 minutes ago -
An incline weighing 1,106 kg with its passengers travels uphill
800 meters on a 30 degree...
asked 17 minutes ago -
Let’s assume you want to retire with $1,000,000 in your
investment portfolio. Given that your investment...
asked 18 minutes ago -
profit motivation is one of the biggest differences between
public and private organizations. what about resource...
asked 17 minutes ago -
Test the hypothesis using P-value approach. Be sure to verify
the requirements of the test.
H0:...
asked 19 minutes ago