The Lotka-Volterra predator-prey model
The Lotka-Volterra predator-prey model
The Lotka-Volterra predator-prey model
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<strong>Lotka</strong>-<strong>Volterra</strong><br />
dR<br />
dt<br />
= (r − λP ) R<br />
dP<br />
dt<br />
= (eλR − m) P<br />
Model with <strong>predator</strong>/<strong>prey</strong> activities<br />
dR<br />
dt<br />
= (r 1 u + r 2 − (λ 1 u + λ 2 v)P ) R<br />
dP<br />
dt<br />
= (e (λ 1 u + λ 2 v)R−(m 1 + m 2 v)) P<br />
Parameter<br />
<strong>prey</strong> per capita<br />
growth rate<br />
interaction strength<br />
conversion of <strong>prey</strong><br />
to new <strong>predator</strong>s<br />
<strong>predator</strong> mortality<br />
rate<br />
<strong>Lotka</strong>-<br />
<strong>Volterra</strong><br />
r constant<br />
λ constant<br />
e constant<br />
m constant<br />
Model with <strong>predator</strong>/<strong>prey</strong> activities<br />
r 1 u+r 2<br />
λ 1 u+ λ 2 v increases with <strong>prey</strong> & <strong>predator</strong><br />
activity<br />
e constant<br />
increases with <strong>prey</strong> activity<br />
m 1 + m 2 v increases with <strong>predator</strong><br />
activity
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