Open AccessDISCONTINUOUS FORCING OF PERIODIC SOLUTIONS IN C 1 VECTOR FIELDS WITH APPLICATIONS TO POPULATION MODELS
Author(s) -
Buchanan J. Robert
Publication year - 1998
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1998.tb00115.x
Subject(s) - forcing (mathematics) , mathematics , population , ordinary differential equation , mathematical analysis , amplitude , norm (philosophy) , population model , differential equation , physics , demography , quantum mechanics , sociology , political science , law
Averaging methods are used to compare solutions of two‐dimensional systems of ordinary differential equations with constant or periodic forcing. The asymptotic separation of solutions of the periodically forced equations from the solutions of the constantly forced equations is proportional to the L 1 norm of the periodic forcing terms. This result is applied to population models of Kolmogorov‐type with climax fitness functions 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.