201

CHAPTER 2

Linearity and Nonlinearity

SECTION 2.6

Systems of DEs: A First Look

where a = b = c = e = 1, d = 0.5 , we have the equilibrium points (0, 0), (1, 0), and (0.5, 0.5). If we draw two nullclines; v-nullcline: y = 1 − x , h-nullcline: x = 0.5 , as shown following we see that the equilibrium point (0.5, 0.5) is unstable. Hence, the two species cannot coexist. y

y

h-nullcline

1.5

1.5

υ -nullcline 0

0

d/e

x 1.5

1/b

Nullclines and equilibria for

1 b

>

0

d

1

Basins of Attraction

27.

(

) , 1( 2

2

) ⎞⎟ ≈ (0.38, 0.60).

5 −1

1 b



shows the basis of the stable equilibrium at

1/b

Sample trajectories for

b

⎛1 1− 5 ⎜ ⎝4

d/e

e

The reader must check separately the cases where

x 1.5

0

=

d e

or

1 d < . b e

>

d e

201

Solutions manual for differential equations and linear algebra 2nd edition by farlow ibsn 9780134689

Solutions Manual for Differential Equations and Linear Algebra 2nd Edition by Farlow IBSN 9780134689548 Full clear download( no error format...

Solutions manual for differential equations and linear algebra 2nd edition by farlow ibsn 9780134689

Solutions Manual for Differential Equations and Linear Algebra 2nd Edition by Farlow IBSN 9780134689548 Full clear download( no error format...