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}

1

2

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.