Initial Conditions, Sources, Sinks, Nodes and Bifurcation

Our problem is to determine which values of D result in extinction and which result in survival. This can be done by studying equation (*), treating D as a bifurcation parameter see Section 2.6

a. Using technology to study solutions to an equation (*) for parameter values of 08, 0.7, 0,4, and 0.5. For each choice of D, use several diflerent initial conditions x0. What are your observations?

b. Find the equilibrium solutions ... as a function of the parameter D and determine whether they are sinks, sources, or nodes. (Assume that the only meaningful equilibrium solutions are those for which 0 < x < 10.) Construct the bifurcation diagram for equation (9. (Sec Section 2.6.) At what value of I) does a bifurcation occur? Explain the significance of this bifurcation with regard to the fate of the H coil.

c. Use technology to test the validity of your bifurcation analysis in part (b) by examining the olutions of equation (*) again, choosing various values of D very close to the bifurcation value you found in part (b). Are your observations as expect?

d. Assuming that the growth vessel is kept at volume of 20 liters, at what speed should the chemostat pump be run in order to maintain a steady-state E. coil population of 8 microgram/liter? A population of 4.5 microgram/liter?

I am really having trouble with this course on Differential Equations. The book that we are using is A Modern Introduction to Differential Equations by Henry Ricardo.

here x(t) denotes the concentration of E.coli at time t. D is the pump rate divided by the volume. This makes sense that when D will be zero the concentration of E.Coli. will completely depend on time and that is what this equation shows.

To begin, we notice that x = 0 is always a solution. ...

Solution Summary

Differential Equations, Initial Conditions, Sources, Sinks, Nodes and are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

I need help trying to find the answer. I have tried about 20 different constraints and all of them are wrong. I don't know what I am doing wrong. Some of the constraints that I have tried are x4 + x6 = 175 and x6 + 0 = 175 just to give you an idea of the way that I am thinking. Evidently it is wrong. Please guide me in the

Please see the attached file for the fully formatted problems.
22. (a) Use PhaseLines to investigate the bifurcation diagram for the differential equation
....
where a is a parameter. Describe the different types of phase lines that occur.
(b) What are the bifurcation values for the one-parameter family in part (a)?
(c) U

One method of checking calculations in volving interconnected circuit elements is to see that the total power delivered equals the total power absorbed...
Please see attached.

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Show that if binary tree T is full at level i, then it is full at every level j smaller than i.
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Show that the depth of the complete binary tree Tn for a general n is given by
D(Tn) = [log2n].
See attached for better format.
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Using induction, give a direct proof of Propo

4.15 Show that this theorem 1 is sharp, that is, show that for infinitely many n>=3 there are non-hamiltonian graphs G of order n such that degu+degv>=n-1 for all distinct nonadjacent u and v.
Can you explain this theorem,please
Theorem1: If G is a graph of order n>=3 such that for all distinct nonadjacent vertices u and

The nodes of a standing wave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move).
Consider a standing wave

Consider the following network.
a) With the indicated link costs, use Dijkstra?s shortest path algorithm to compute the shortest path from E to all network nodes. Show how the algorithm works by computing a table.
b) Eliminate node A, and redo the problem starting from node B.
Please refer to the attachment to view the

1. In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodesand between all intermediate nodesand all destinations for a given transshipment problem. In addition, ass