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The Lotka-Volterra predator-prey model

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dS 1<br />

dt<br />

dS 2<br />

dt<br />

dC<br />

dt<br />

= − 1 Y 1<br />

S 1<br />

K 1 + S 1<br />

u 1 C<br />

= − 1 S 2<br />

u 2 C<br />

Y 2 K 2 + S<br />

( 2<br />

µ1 S 1<br />

=<br />

u 1 + µ )<br />

2S 2<br />

u 2 C<br />

K 1 + S 1 K 2 + S 2<br />

u 1 =<br />

{ 1 when<br />

µ 1 S 1<br />

K 1 +S 1<br />

> µ 2S 2<br />

K 2 +S 2<br />

0 when<br />

µ 1 S 1<br />

K 1 +S 1<br />

< µ 2S 2<br />

K 2 +S 2<br />

µ 1 S 1<br />

K 1 +S 1<br />

= µ 2S 2<br />

K 2 +S 2

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