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Permanence and extinction for a nonlinear diffusive predator-prey system. (English) Zbl 1173.34033
Recent epidemics (e.g. SARS, Avian flu and H1N1 flu) has shown the importance of including nonlocal effects in epidemics. This makes this paper important. The authors consider a non-autonomous predator-prey system in a poor patchy environment. Under the assumption that the intrinsic growth rates of the species may be negative, sufficient conditions are obtained for the permanence and extinction of the system considered. Both single species and predator-prey cases are studied.
MSC:
34D05Asymptotic stability of ODE
92D25Population dynamics (general)