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Volume 14,     Number 2,     Summer 2006

 

NICHOLSON'S BLOWFLIES EQUATION
WITH A DISTRIBUTED DELAY
ELENA BRAVERMAN AND DAMIR KINZEBULATOV

Dedicated to Jack W. Macki and James S. Muldowney
on the occasion of their retirement

Abstract. For the Nicholson's blowflies equation with a distributed delay
                               
we obtain existence, positiveness and permanence results for solutions with positive initial conditions. We prove that all nonoscillatory about the positive equilibrium N* solutions tend to N*. In the case δ < p < δe there are no slowly oscillating solutions and the positive equilibrium is globally asymptotically stable. Some generalizations to other nonlinear models of population dynamics with a distributed delay in the recruitment term and a nondelayed linear death term are considered.

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© 2006, Canadian Applied Mathematics Quarterly (CAMQ)