Consider again the system dx/dt = x(1 − x − y), (i) dy/dt = y(0.75 − y − 0.5x), which appeared in Example 1 of Section 7.3. A constant-effort model, applied to the species x alone, assumes that the rate of growth of x is altered by including the term −Ex, where E is a positive constant measuring the effort invested in harvesting members of species x. This assumption means that, for a given effort E, the rate of catch is proportional to the population x, and that for a given population x the rate of catch is proportional to the effort E. Based on this assumption, Eqs. (i) are replaced by dx/dt = x(1 − x − y) − Ex = x(1 − E − x − y), dy/dt = y(0.75 − y − 0.5x). (ii) (c) Draw a direction field and/or a phase portrait for E = E0 and for values of E slightly less than and slightly greater than E0.

Using mathematical software such as MATLAB, Python with matplotlib, or other graphing tools to plot the direction field and phase portrait based on the given equations and parameters.

To draw a direction field and/or a phase portrait for the given system of equations, we need to plot representative vectors in the x-y plane based on the given differential equations. The vectors will indicate the direction of the solutions at different points.

Let's first draw the direction field for E = E0, where E0 is a constant effort.

Direction Field:

To plot the direction field, we choose a grid of points in the x-y plane and calculate the corresponding vectors based on the given differential equations.

Choose a suitable range for x and y, and divide the range into small intervals or grid points. For example, let's choose the range -1 ≤ x ≤ 2 and -1 ≤ y ≤ 2, and divide the range into intervals of 0.2.

For each grid point (x, y), calculate the values of dx/dt and dy/dt using the given equations dx/dt = x(1 − E − x − y) and dy/dt = y(0.75 − y − 0.5x). These values will give us the components of the vectors at each point.

Plot arrows or line segments at each grid point with lengths proportional to the magnitude of the vectors and directions indicating the direction of the vectors.

Repeat this process for multiple grid points to cover the entire range and obtain a representative direction field.

Phase Portrait:

To draw the phase portrait, we need to plot the trajectories or solutions of the differential equations in the x-y plane.

Choose a set of initial conditions (x0, y0) and solve the differential equations numerically or graphically to obtain the trajectories or solution curves. Use different initial conditions to explore different behaviors of the system.

Plot the obtained trajectories or solution curves on the x-y plane.

Repeat this process for different sets of initial conditions to get an overall view of the phase portrait.

Note that for values of E slightly less than and slightly greater than E0, you can repeat the above steps with the corresponding values of E to observe any changes in the direction field or phase portrait.Unfortunately, I am unable to generate visual plots directly in this text-based format. I suggest using mathematical software such as MATLAB, Python with matplotlib, or other graphing tools to plot the direction field and phase portrait based on the given equations and parameters.

To know more about MATLAB.

https://brainly.com/question/15071644

#SPJ11

what is 3/7 as decimal

help i dont understand how to do this the question is "Put your answer in decimal form."

Help me please I am a idiot who doesn’t get math

Write each ratio in three different ways based on the table. Party Mix Makes 8 Cups 3 cups pretzels 3 cups bagel chips 1 cup cheese crackers 1 cup peanuts

Write a similarly comparing the three triangles in the diagram

A cell phone costs $750 and loses 28% of its value each year. Write an exponential decay function to represent this situation.

1. f(x)= 750 • 0.72^x
2. f(x)= 0.72 • 750^x
3. f(x)= 750 • 0.28^x
4. f(x)= 0.28 • 750^x

Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.

simplify
(in attachment)

hi help again lol :)​

which of the given values will make the inequality n-93>175 true?

n=82
n=105
n=268
n=300
n=312

PLEASE HELPP!!!!

ive been stuck on this for 3 days i feel clueless

what's
[tex](4 \sqrt{2} ) {}^{2} [/tex]
​

Solve the system of linear equations by elimination x + 2y = 13 --x+y=5​

Select the three inequalities that have n = 3 in the solution set
A. n + 5 < 9
B. 13 n < 1
C. 3n + 1 >7
D. 3n > 9.5
E. n-2<5

A lumberjack needs to climb a tree to place a satellite tower in the tree top in the woods. The satellite signal needs to reach a horizontal distance of 3500 meters along the ground. If the angle of elevation from the farthest distance along the ground that the satellite reaches to the satellite in the tree is 18 degrees, what is the radius of the satellite signal? Round your answer to the nearest meter.

Radius of the satellite signal = meters

Given the expression below, identify its factors.

3a + 4b– 7c - 12

Steve studies math for 7/8 of an hour and history for 2/3 of an hour. How many hours did he study?

A sum of money is divided between Mohan and Sohan in the ratio 5:7 . If Sohan's share is ₹665, find the total amount.​
please help me fast.

3
Gürkan bisikletiyle birinci gün 3.1 km, ikinci gun 4.5 km ve puncu
gun 4.25 km yol almıştır Gürkan üç günde toplam kaç km yol aims
tir? Tahmin ediniz Tahmininizi işlem yaparak kontrol ediniz.
​

what kind of number is e?

a.) integer
b.) rational
c.) natural
d.) irrational

Which shows the numbers ordered from least to greatest? 9.129, 9.37, 9.3, 9.219

The Milgram Family drove 440 miles on 20 gallons of gas. At this rate, how many miles can they drive on 25 gallons of gas? *

Each pair of polygons is similar. Find each missing side measure. two polygons 12 on top 5 on bottom second polygon 48 on top x on bottom

A scale model of a house is 1/10 the size of the actual house. One of the bedrooms in the house is 16 feet long. Which expression will help you find the length of the same bedroom in the model?

Determine if the two triangles are congruent.

math help me pls now now

Complete the sentence.

Model the unknown number problem by writing an
algebraic expression. Then complete the statements.
Juan doubled his workout time.
Replace the words 'workout time" with.
The word "doubled" means
The correct algebraic expression is

What is the solution of the system of equations? Enter the solution as an ordered pair (use decimal rounded to the nearest hundredth if necessary)

=32+54−2+8=−25

What is the value of x

help me plz !!!!!!!!!!