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Global attractivity and oscillation in a periodic “food limited” population model with delay. (Chinese. English summary) Zbl 1081.34523

Summary: The nonlinear delay differential equation \[ N'(t)=r(t)N(t) \left(\frac{K(t)-N(t-m\omega)}{K(t)+\lambda(t)N(t-m\omega)}\right), \] where \(m\) is positive integer, \(\lambda(t)\), \(K(t)\) and \(r(t)\) are positive periodic functions of period \(\omega\). Sufficient conditions for oscillation, existence and global attractivity of a positive periodic solution of this equation are obtained. Some known results are extended and improved.

MSC:

34K13 Periodic solutions to functional-differential equations
34K11 Oscillation theory of functional-differential equations
92D25 Population dynamics (general)
34K20 Stability theory of functional-differential equations
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