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A simple population model with qualitatively uncertain dynamics

Neubert1

  • 1Biology Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, U.S.A.

Journal of Theoretical Biology
|March 7, 1998
PubMed
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Nonlinear systems can exhibit "riddled" basins of attraction, making population survival unpredictable. This unpredictability surpasses that of chaotic systems with fractal boundaries, impacting ecological modeling.

Area of Science:

  • Ecology
  • Nonlinear Dynamics
  • Mathematical Biology

Background:

  • Basins of attraction in nonlinear systems can be 'riddled,' meaning nearby points lead to different attractors.
  • This complex basin structure introduces a high degree of unpredictability in system dynamics.

Purpose of the Study:

  • To investigate the presence and implications of riddled basins of attraction in ecological models.
  • To demonstrate how riddled basins create a unique form of unpredictability in population dynamics.

Main Methods:

  • Development of two single-species population models.
  • Incorporation of chaotic forcing into the population models.
  • Analysis of the resulting basins of attraction to identify 'riddled' structures.

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Main Results:

  • Two chaotically forced single-species population models were found to possess riddled basins of attraction.
  • The complex basin structure leads to effective unpredictability in the ultimate survival of these populations.
  • This unpredictability is qualitatively greater than that associated with standard chaotic attractors or fractal basin boundaries.

Conclusions:

  • Riddled basins of attraction represent a significant source of unpredictability in ecological systems.
  • The findings highlight the limitations of predicting population survival in systems with complex nonlinear dynamics.
  • Further research into nonlinear dynamics is crucial for understanding complex ecological phenomena.