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Theoretical Population Biology 62, 121128 (2002) doi:10.1006/tpbi.2002.1584
 

Summary: Theoretical Population Biology 62, 121128 (2002)
doi:10.1006/tpbi.2002.1584
Population Dynamics with a Refuge: Fractal Basins and
the Suppression of Chaos
T. J. Newman
Department of Physics and Department of Biology, University of Virginia, Charlottesville, Virginia 22903
and
J. Antonovics and H. M. Wilbur
Department of Biology, University of Virginia, Charlottesville, Virginia 22903
Received January 20, 2001
We consider the effect of coupling an otherwise chaotic population to a refuge. A rich set of dynamical
phenomena is uncovered. We consider two forms of density dependence in the active population: logistic
and exponential. In the former case, the basin of attraction for stable population growth becomes fractal,
and the bifurcation diagrams for the active and refuge populations are chaotic over a wide range of
parameter space. In the case of exponential density dependence, the dynamics are unconditionally stable
(in that the population size is always positive and finite), and chaotic behavior is completely eradicated for
modest amounts of dispersal. We argue that the use of exponential density dependence is more
appropriate, theoretically as well as empirically, in a model of refuge dynamics. & 2002 Elsevier Science (USA)
Key Words: seed bank; dormancy; chaos; dispersal; spatial ecology; logistic map; exponential map
1. INTRODUCTION

  

Source: Antonovics, Janis - Department of Biology, University of Virginia

 

Collections: Biology and Medicine