The Lotka-Volterra predator-prey model
The Lotka-Volterra predator-prey model
The Lotka-Volterra predator-prey model
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LetR n = G 1 ∪ G 2 ∪ M<br />
Filippov definition of a solution<br />
(Filippov 1960, 1985)<br />
{<br />
dx f<br />
dt = 1 (x) x ∈ G 1<br />
f 2 (x) x ∈ G 2<br />
(DR)<br />
F (x)≡<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
{f 1 (x)} x ∈ G 1<br />
conv{lim y∈G 1<br />
y→x<br />
f 1 (y), lim y∈G 2<br />
y→x<br />
f 2 (y)}<br />
x ∈ M<br />
{f 2 (x)} x ∈ G 2<br />
dx<br />
dt ∈ F(x)<br />
(DI)<br />
Definition: Solutions of differential equation (DR) in the Filippov sense are<br />
solutions of differential inclusion (DI)
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