Math 2280-2
Example 6.1.1 Squirrel and Rabbit population
with(DEtools):
ics:=[[x(0)=8,y(0)=2], [x(0)=2,y(0)=8], [x(0)=2,y(0)=2],[x(0)=8,y(0)=6],[x(0)=1,y(0)=4],[x(0)=3,y(0)=9],[x(0)=6,y(0)=1]];
phaseportrait([diff(x(t),t) = 14*x(t) - 2*x(t)^2 - x(t)*y(t),
diff(y(t),t) = 16*y(t) - 2*y(t)^2 - x(t)*y(t)],
[x(t),y(t)], t=0..2,ics
,
stepsize=1/100, x=-1..10,y=-1..10,
linecolor=black, dirgrid=[30,30]);
Linearization around the equilibrium (4,6)
with(LinearAlgebra): with(plots):
A:=Matrix(2,2,[-8,-4,-6,-12]);
evalf(Eigenvectors(A));
fieldplot([-8*u-4*v,-6*u-12*v], u =-0.1..0.1,v=-0.1..0.1,color=black);
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