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Uniform persistence in multispecies population models. (English) Zbl 0631.92012
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.
Reviewer: M.Brokate

MSC:
92D25 Population dynamics (general)
37-XX Dynamical systems and ergodic theory
34D20 Stability of solutions to ordinary differential equations
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