Uniform persistence in multispecies population models (Q1095067)

The author considers an ODE system \(\dot x_ i=x_ if_ i(x)\) and gives a sufficient condition for uniform persistence which only involves upper and lower bounds of \(f_ i\) and \(\partial_ jf_ i\) on a suitably chosen compact set B. To prove this, he exhibits explicitly a persistence function which satisfies the conditions of a more abstract theorem. He also applies his theorem to certain food chains.