Question: Analyze the models for competition between two species given in Problems, using the following outline. (a) Find and plot the equilibrium points and nullclines. Determine

Analyze the models for competition between two species given in Problems, using the following outline.
(a) Find and plot the equilibrium points and nullclines. Determine the directions of the vector fields between the nullclines.
(b) Decide whether the equilibrium points are unstable (repelling at least some nearby solutions) or stable (repelling no nearby solutions).
(c) Sketch portions of solution curves near equilibrium points: then complete the phase p malt of the system.
(d) Decide whether the two species described by the model can coexist. What conditions are required for coexistence when it is possible?
dx/dt = x(4 - 2x - y)
dy/dt = y(4 - x - 2y)

Step by Step Solution

★★★★★

3.35 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a x x4 2x y y y4 x 2y Setting x 0 and y 0 we find vnullc... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

947-M-L-A-L-S (4653).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Two species of predatory Birds-collard flycatchers and tits-compete for nest holes during breeding season on the island of Gotland, Sweden. Frequently, dead flycatchers are found in nest boxes...

The Delta Wire Corporation was founded in 1978 in Clarksdale, Mississippi. The company manufactures high-carbon specialty steel wire for global markets and at present employs about 100 people. For...

For the competition model dx/dt = x(a - bx - cy). dy/dt = y(d - ex - fy), Where the parameters a, b, c. d, e, and f are all positive, the diagrams in Problems show four possible positions of the...

I have literally posted the complete assignment information, can I please have some help with these two problems? MAT 375 Module Two Guided Activity: (Continuous) Dynamical Systems Our textbook has a...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

6. Let D be the size of a population of deer, and M the population of moose in the same area. The LotkaVolterra competition model for these species might look like the following: 0" = 0.30 0.0202...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

Jupyter NoteBook Once we decide to measure more than three features per input vector, it can become challenging to understand how a network is learning to solve such a problem since we can no longer...

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

Here is the budword_part1.m file Here is budword_part2.m file Here is the euler file 1 Background The background information is from the book Mathematical Biology by J.D. Murray 2. The spruce budworm...

Back in the Old Days text adventure games were a popular genre of computer games. These games had an interface that is reminiscent of command line interfaces. During a project in your computer...

Classify each of the following as a field, record, or file interrogation: a. Limit check b. Validity check c. Version check d. Missing data check e. Sign checks f. Expiration date check g....

True or False: The GASB requires disclosures related to three types of credit risk.

(Short-Run Loss) Suppose a firm decides to shut down in the short run. What is the resulting loss?

Let V be the set of all infinite sequences {x n } = {x 1 , x 2 , x 3 , ....} of real numbers. Let addition of elements of V and multiplication by scalars be defined as follows: and (a) Show that V is...

In Problems 2528, express the vector t as a linear combination of the vectors u, v, and w. t = (7,7,7), u = (2, 5, 3), v = (4, 1, -1), w = (1, 1, 5)

In Problems 2528, express the vector t as a linear combination of the vectors u, v, and w. t = (0, 0, 19), u = (1,4,3), v = (-1, -2,2), w = (4,4, 1)

Subject - Introduction to Investment Management. Project Topic: Segregated Funds Segregated Funds: - Segregated funds are sold by a particular group in Canada. Who has the ability to sell segregated...

Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 434 people age 65 and over, 106 of them...

2. Judy Johnson is choosing between investing in two Treasury secu- rities that mature in five years and have par values of $1,000. One is a Treasury note paying an annual coupon of 5.06 percent. The...