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.