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Aaron King

       Aaron A. King, Ph.D.

      Assistant Professor of Ecology & Evolutionary Biology and Mathematics
      University of Michigan
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UM Library 		Subharmonic Resonance and Multi-annual Oscillations in northern Mammals

Subharmonic resonance and multi-annual oscillations in northern mammals: a nonlinear dynamical systems perspective

W. M. Schaffer, B. S. Pederson, K. Moore, O. Skarpaas, A. A. King, and T. V. Bronnikova

Chaos, Solitons, & Fractals, 12: 251-64, 2001.

Abstract

The multi-annual oscillations of northern mammals represent one of ecology's most celebrated patterns. In a recent review of the subject, K. Norrdahl proposed that the cycles Average rotation number on a chaotic attractor result from the interaction of victim herbivores and their specialist predators, with the intrinsic time scale of the prey species setting the period of the oscillation. As biologists, we find this hypothesis appealing because it offers a spartan accounting of the principal observations. As theoreticians, we find it attractive because it articulates, in the main, just those conclusions to which one is led by considering the problem from the perspective of dynamical systems theory. Specifically, we believe that northern mammal cycles are most plausibly interpreted as ecological examples of a ``subharmonic resonance''.

For reprints of this paper, contact me at aaron.king@umich.edu. An electronic reprint (PDF) is also available.