The Lotka-Volterra predator-prey model

C⊣⊓⌋〈†√∇≀⌊↕⌉⇕⇐∞⇒
C⊣⊓⌋〈†P⌉⊣\≀⊑⊣⊔〈⌉≀∇⌉⇕¬C≀\⊔〉\⊓〉⊔†≀{fI↽⌉§〉∫⊔⌉\⌋⌉≀{∫≀↕⊓⊔〉≀\∫≀{⊔〈⌉
C⊣⊓⌋〈†P⌉⊣\≀⊑⊣⊔〈⌉≀∇⌉⇕¬C≀\⊔〉\⊓〉⊔†≀{fI↽⌉§〉∫⊔⌉\⌋〉⌉\∇≀⊑\〉⌋⌉⇐∞⇒
Existence of solutions for ODEs
dx
dt
x(0) = x 0
= f(t, x(t))
(1)
x = (x 1 , . . . , x n ) a f : I × D ⊂ R × R n → R n .
Cauchy-Peano theorem: Continuity of f =⇒ existence of solutions to the Cauchy
problem (1)