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    Author(s): James F. Selgrade
    Date: 1998
    Source: Journal of Difference Equations and Applications, 1998, Vol. 4, pp. 163-183
    Publication Series: Miscellaneous Publication
    PDF: View PDF  (392 KB)

    Description

    This study considers a general class of 2-dimensional, discrete population models where each per capita transition function (fitness) depends on a linear combination of the densities of the interacting populations. The fitness functions are either monotone decreasing functions (pioneer fitnesses) or one-humped functions (climax fitnesses). Four sets of necessary inequality conditions are derived which guarantee generically that an equilibrium loses stability through a period-doubling bifurcation with respect to the pioneer self-crowding parameter. A stocking or harvesting term which is proportional to the pioneer density is introduced into the system. Conditions are determined under which this stocking or harvesting will reverse the bifurcation and restabilize the equilibrium. A numerical example illustrates how pioneer stocking can be used to reverse a period-doubling cascade and to maintain the system at any attracting cycle along the cascade.

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    Citation

    Selgrade, James F. 1998. Using Stocking or Harvesting to Reverse Period-Doubling Bifurcations in Discrete Population Models. Journal of Difference Equations and Applications, 1998, Vol. 4, pp. 163-183

    Keywords

    discrete models, period-doubling bifurcations and reversals, pioneer and climax populations

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