Question: Try to draw a phase-line diagram with two stable equilibria in a row. Use the Intermediate Value Theorem to sketch a proof of why this

Try to draw a phase-line diagram with two stable equilibria in a row. Use the Intermediate Value Theorem to sketch a proof of why this is impossible.
The fact that the rate-of-change function is continuous means that many behaviors are impossible for an autonomous differential equation.

Step by Step Solution

★★★★★

3.30 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose there are two stable equilibria in a row Then the rate of cha... 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)

808-C-D-E (1039).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Give an equation like Equation 5.8.2 describing a system with two thresholds. The system has a stable equilibrium at a resting potential at 0, but will be pushed to a higher positive equilibrium if...

Why is it impossible for a solution of an autonomous differential equation to oscillate? The fact that the rate-of-change function is continuous means that many behaviors are impossible for an...

Use the Intermediate Value Theorem to prove that (cos t)t3 + 6 sin5 t - 3 = 0 has a real solution between 0 and 2.

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

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,...

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...

Prof. ll June 14, 2016 MAT224: Differential Equations Existence and Uniqueness of Solutions Consider the Initial Value Problem: y (x) = f (x, y) y(x0 ) = y0 . It would be good to know if a solution...

\fCHAPTER 14 Server Farms: M/M/k and M/M/k/k In today's high-volume world, almost no websites, compute centers, or call centers consist of just a single server. Instead a \"server farm\" is used. The...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Carefully collect data cross-classified by two categorical variables for which you are interested in determining whether there is a relationship. Do not get the data from a book, website, or journal;...

1. How many different possible permutations can be made from the word MAGTUBA such that the vowels will never be together? A. 1, 200B. 1, 080 C. 980 D. 840 2. In a meeting, it is required to seat 3...

Using Accelerated Depreciation which of the following has primary financial advantage for the firm: Reporting assets at a greater value Net income is greater during early years of depreciated assets...

Draw a Venn diagram. Draw a Venn diagram that shows the relation between the events A and B in Exercise 4.70. Indicate each of the following events on your diagram and use the information in Exercise...

Continuation of Exercise 4-124. Determine the cumulative distribution function of the random variable.

Continuation of Exercise 4-124. Determine the mean and variance of the random variable.

The time between calls is exponentially distributed with a mean time between calls of 10 minutes. (a) What is the probability that the time until the first call is less than 5 minutes? (b) What is...

Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%,...

eBook Problem Walk-Through Cost of Equity: Dividend Growth Summerdahl Resort's common stock is currently trading at $37 a share. The stock is expected to pay a dividend of $2.75 a share at the end of...

Dividendos por accin Oceanic Company tiene 25,000 acciones preferentes acumulativas del 3%, par $50 y 50,000 acciones comunes de par $10. En concepto de dividendos se distribuyeron las siguientes...