Question
In: Advanced Math
Consider the following model of interacting species: R' = R(2 + 3R − S) S' =...
Consider the following model of interacting species:
R' = R(2 + 3R − S)
S' = S(1 − S + 4R)
(a) Find all the equilibrium points, and determine the type of those points which are in the first quadrant (including those on the axes)
(b) Plot the phase portrait of the system.
(c) If the initial conditions are R(0) = 1 and S(0) = 1, what will be the population size of each species when t → ∞?
Solutions
Colby Messinger answered 1 year agoRelated Solutions
L = {a r b s | r, s ≥ 0 and s = r 2}....
L = {a r b s | r, s ≥ 0 and s = r 2}. Show that L is not regular
using the pumping lemma
Q3. Consider the following data: S = 100; r = .08; s = .3 on the...
Q3. Consider the following data: S =
100; r = .08; s = .3 on the
following two options:
Call 1 Call 2
K = 100; K = 90
T-t=90 days. T-t=180 days.
Price: 6.91 16.33
Delta: .58
.78
Gamma: .02
.0138
3.1 A trader just shorted 100 CBOE calls 2.
Calculate the number of shares necessary to create a
Delta Neutral position.
3.2 A trader just shorted 100 CBOE calls 2.
Calculate the number of calls 1...
Given H = (3R^2/ sin θ) aθ + 54 R cos θ aφ A/m (a) Find...
Given H = (3R^2/ sin θ) aθ + 54 R cos θ aφ A/m (a) Find J.
(b) Find the total current in the aθ direction through the
conical surface θ = 20◦, 0 ≤ φ ≤ 2π, 0 ≤ R ≤ 5
Please explain (b) thoroughly.
Consider the following species: Na, Mg, Cl^-1,S,Cl,Ar,Na^+ (a) Order the above species in order of increasing...
Consider the following species: Na, Mg, Cl^-1,S,Cl,Ar,Na^+
(a) Order the above species in order of increasing atomic/ionic
radius.
(b) Order the above species in order of increasing electron
affinity
Consider the following Neoclassical model of economy, where thedomesticinterest rate r and the world...
Consider the following Neoclassical model of economy, where the
domesticinterest rate r and the world interest rate r * are in percentage
terms. 20 (Marks)Supply: Y= 2000NX= 200-200r * = 5%Demand: C = 200+ 0.8 (Y-T)I= 400- 20rG= 0, T = 0(a) Find the equilibrium real interest, national saving, and
investment in a closedeconomy with no public sector. Show the equilibrium real interest
rate on asaving-investment diagram with r measured on the vertical
axis.(b) Now assume the small economy opens...
Consider the following Neoclassical model of economy, where thedomesticinterest rate r and the world...
Consider the following Neoclassical model of economy, where the
domesticinterest rate r and the world interest rate r * are in percentage
terms. 20 (Marks)Supply: Y= 2000NX= 200-200r * = 5%Demand: C = 200+ 0.8 (Y-T)I= 400- 20rG= 0, T = 0(a) Find the equilibrium real interest, national saving, and
investment in a closedeconomy with no public sector. Show the equilibrium real interest
rate on asaving-investment diagram with r measured on the vertical
axis.(b) Now assume the small economy opens...
Consider N massless non-interacting spin-s fermions in a three-dimensional box of volume V . (a) Find...
Consider N massless non-interacting spin-s fermions in a
three-dimensional box of volume V .
(a) Find the Fermi energy EF as a function of N, V , and
s.
(b) For zero temperature, find the pressure in terms of N, V , and
EF .
(c) Plot the occupation of states as a function of the energy at a
temperature of T =EF /(10k). Your graph can be a sketch
by hand. However, the effect of the finite temperature should...
Consider the species (O2)2- and (O2)2+. According to molecular orbital theory, which of these species will...
Consider the species (O2)2- and (O2)2+. According to molecular
orbital theory, which of these species will be diamagnetic?
(O2)2+ and (O2)2-
(O2)2+
(O2)2-
neither is diamagnetic
The magnetic property can only be determined for molecules, not
ions.
Let L = {0 r | r = s 2 , s a positive integer}. Give...
Let L = {0 r | r = s 2 , s a positive integer}. Give the
simplest proof you can that L is not regular using the pumping
lemma.
Consider the following growth model and answer the questions below. (1) S=I (2) S=sY (3) Y=F(K,AL),...
Consider the following growth model and answer the questions
below.
(1) S=I
(2) S=sY
(3) Y=F(K,AL), λY=F(λK,λAL)
(4) K^'=I-δK 0<δ<1
(5) L^'=nL n>0
(6) A^'=gA g>0
Endogenous (6): , , , , ,
Predetermined (3): K, L, A
Initial Conditions (3): K_0, L_0, A_0
Exogenous (5): n, g, s, δ
1. Show that equations (1)-(6) reduce to the two intensive form
equations
y=f(k)
k^'=sy-[n+g+δ]k
where k=K/AL , y=Y/AL
2. Show in a diagram how an increase in the rate of...
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