Question

dx/dt = 4x -x^2 -2xy

dy/dt = -y+0.5 xy

a) find equilibrium points

b) find Jacobian matrix for above system

c) find Jacobian matrix at eq. point (0,0)

d) draw phase portrait near (0,0) from ©

e) show at eq. point (4,0) the Jacobian matrix is

-4 -8

0 1

f) draw phase portrait near (4,0) from (d)

g) at eq. point (2,1) the Jacobian matrix is

-2 -4

0.5 0

h) draw phase portrait near (2,1) from (f)

i) make global phase diagram using the above three drawings

j) what happens to x and y for large t if

1. the initial conditions x>0, y>0

2. the initial conditions x>0, y=0

3. the initial conditions x=0, y>0

Answer 1

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