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Average growth and total permanence in a competitive Lotka-Volterra System. (English) Zbl 1162.34329

Summary: We consider a class of non-autonomous competitive Lotka-Volterra Systems. Such a system is called strongly permanent if small perturbations of the system are permanent. We define such a system to be totally permanent if the system as well as its subsystems are strongly permanent. When the growth rates have averages and the interaction coefficients are non-negative constants, we give a computable necessary and sufficient condition for the system to be totally permanent.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
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