Population dynamics with a refuge: fractal basins and the suppression of chaos

TY - JOUR

T1 - Population dynamics with a refuge

T2 - fractal basins and the suppression of chaos

AU - Newman, T. J.

AU - Antonovics, J.

AU - Wilbur, H. M.

PY - 2002/9/1

Y1 - 2002/9/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0036727595

U2 - 10.1006/tpbi.2002.1584

DO - 10.1006/tpbi.2002.1584

M3 - Article

AN - SCOPUS:0036727595

SN - 0040-5809

VL - 62

SP - 121

EP - 128

JO - Theoretical Population Biology

JF - Theoretical Population Biology

IS - 2

ER -