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Hopf bifurcation in pioneer-climax competing species models. (English) Zbl 0859.92025

Summary: Two-dimensional pioneer-climax models of competing species differential equations are introduced and examined. The per capita growth rates are functions of weighted densities of the individual species. Constant rate forcing is added representing stocking or harvesting. The ensuing stability properties of interior equilibria are studied. The primary interest is when stable periodic behavior of the populations results from a Hopf bifurcation. For linear and quadratic fitnesses, general formulas are calculated for determining the stability of the periodic orbit and for finding the Hopf bifurcation surface. Also strategies for restoring the system to a stable equilibrium are developed.

MSC:

92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
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