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Dynamics of a class of non-autonomous systems of two non-interacting preys with common predator. (English) Zbl 1069.34071

The system

y i ' =y i (a i -c i y i -b i y 3 ),i=1,2,
y 3 ' =y 3 (-a 3 +b 3 y 1 +b 4 y 2 ),

with positive, variable coefficients is investigated with respect to permanence, extinction and global stability. For periodic coefficients also periodic solutions are studied.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34C25Periodic solutions of ODE
34D05Asymptotic stability of ODE
34D23Global stability of ODE
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