A unified approach to persistence. (English) Zbl 0669.92020
The author defines the concept of permanence for dynamical systems of the type that might arise from models of ecological systems. He quotes a “geometric” sufficient condition for permanence in Lotka-Volterra systems and uses modern dynamical system theory to give a new proof. Along the way, he works out some interesting results about the asymptotic behaviour of time averages for solutions of Lotka-Volterra equations. As an example, a two-prey two-predator Lotka-Volterra system is analyzed.
Reviewer: A.Hausrath
MSC:
| 92D40 | Ecology |
| 34D20 | Stability of solutions to ordinary differential equations |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
Keywords:
repeller; persistence; Morse decomposition; predator-prey systems; attractor; permanence; Lotka-Volterra systems; asymptotic behaviour of time averagesReferences:
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