The Lotka-Volterra predator-prey model
The Lotka-Volterra predator-prey model
The Lotka-Volterra predator-prey model
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…and this lead him to the Gause <strong>model</strong>…<br />
dR<br />
dt<br />
= rR−Cf(R)<br />
dC<br />
dt<br />
= (ef(R)−m)C<br />
Gause‘s stability criterion: Let (R ∗ , C ∗ ) be an equilibrium of the above <strong>model</strong>.<br />
Provided<br />
df<br />
dR (R∗ ) > f(R∗ )<br />
R ∗<br />
then the equilibrium is locally asymptotically stable.<br />
Destabilizing f<br />
Potentially stabilizing f
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