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Phase Portrait of Lotka-Volterra Equation

​
parameters
a
1
b
1
h
1
k
1
critical points (CP)
(
x
1
,
y
1
) = {0,0}
(
x
2
,
y
2
) = {h/b, k/a}
=
{1,1}
eigenvalues (λ, μ)
at (
x
1
,
y
1
) : (​
λ
1
​,​
μ
1
​) = {-h,k} =
{-1,1}
at (
x
2
,
y
2
: (​
λ
2
​,​
μ
2
​) = -
hk
​,
hk
​​ =
{-,}
stability behavior
at (
x
1
,
y
1
) saddle point
at (
x
2
,
y
2
) center
This Demonstration shows a phase portrait of the Lotka–Volterra equations, including the critical points. The eigenvalues at the critical points are also calculated, and the stability of the system with respect to the varying parameters is characterized.
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