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Volume 7,     Number 4,     Winter 1999

 

DISCONTINUOUS FORCING OF PERIODIC
SOLUTIONS IN n-DIMENSIONAL C1
VECTOR FIELDS WITH APPLICATIONS
TO POPULATION MODELS
J. ROBERT BUCHANAN

Abstract. Averaging methods are used to compare solutions of n-dimensional systems of ordinary differential equations with constant versus periodic forcing. The asymptotic separation of solutions of the periodically forced equations from the solutions of the constantly forced equations is proportional to the sum of the L1 norms of the periodic forcing terms. This result is applied to population models of Kolmogorov-type where forcing represents stocking or harvesting of a population. The asymptotic behavior of such systems may be controlled, to some extent, by varying the period and/or amplitude of the forcing functions.

 

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