Answers to Se lected Exercises 569- T he so lution of case a. spirals outward toward the solution of case b. The
solution of case c. spirals inward toward the solution of case b.
May's Prey-Predator Mo d e l
- The solution of case a. spirals inward toward the solution of case b. The
solution of case c. spirals outward toward the solution of case b.
Competing S pecies Models- a. (80/7, 24/7)
b.
(i) (ii) (iii) (iv)
limt, 00 x(t) ~ 0 20 20 0
limt, 00 y(t) ~ 12 0 0 12
extinct species x y y x - a. (i) None
(ii) 1 - 4 limt, 00 x(t) = 10 limt, 00 y(t) = 0, y becomes extinct.
b. (i) ( 4, 2) (ii) 1 - 4 limt-->oo x(t) = 4 limt__, 00 y(t) = 2
c. (i) None
(ii) 1 - 4 limt__, 00 x(t) = 0 limt__, 00 y(t) = 4, x becomes extinct.Exercises 1 0.6 E p idemics
l. a. 300 c. (i) 8(5) = 232 (ii) 8(5) = 150
3. Yes (i) 8(5) = 148 (ii) 8(5) = 114
Exercises 10. 7 P e n dulums
l. The period varies with Y2(0).
- y~ = Y2
y~ = 2wy4 sin</> - gyif C
Y~ = Y4
Y4 = -2wy2 sin </> - gy3 / Cwhere Y1 = x, Y2 = x', y3 = y , and Y4 = y'.
a. y 3 (6.28) = 0, The plane of oscillation does not appear to rotate.
b. y 3 (6.28) = -3.238823£ - 04; 1.41 days
c. y 3 (6.28) = 3.238823E - 04; 1.41 days