Open AccessSTABLE PERIODIC BEHAVIOR IN PIONEER‐CLIMAX COMPETING SPECIES MODELS WITH CONSTANT RATE FORCING
Author(s) -
Sumner Suzanne
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.tb00306.x
Subject(s) - climax , hopf bifurcation , mathematics , constant (computer programming) , monotonic function , growth rate , forcing (mathematics) , per capita , ecology , mathematical analysis , bifurcation , physics , biology , nonlinear system , geometry , demography , quantum mechanics , population , sociology , computer science , programming language
Two‐dimensional pioneer‐climax models of competing species differential equations are studied where the per capita growth rates are functions of weighted densities of the populations. The per capita growth rate of the pioneer species is monotonically decreasing whereas the per capita growth rate of the climax species is a one‐humped function of the total weighted density. Constant rate forcing is introduced into the model representing stocking or harvesting. General formulas are calculated for determining the stability of the periodic orbit arising from a Hopf bifurcation.