Spatiotemporal Chaos in Easter Island Ecology

J. C. Sprott
Department of Physics
University of Wisconsin, Madison

ABSTRACT

This paper demonstrates that a recently proposed spatiotemporal model for the ecology of Easter Island admits periodic and chaotic attractors, not previously reported. Such behavior may more realistically depict the population dynamics of general ecosystems and illustrates the power of simple models to produce the kind of complex behavior that is ubiquitous in such systems.

Ref: J. C. Sprott,  Nonlinear Dynamics, Psychology, and Life Sciences 16, 387-395  (2012).

The complete paper is available in PDF format.

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Figure 1

Fig. 1. Population density of people (P), rays (R), and trees (T) as a function of time at a fixed position around the ring. Time is in units of years.

Figure 2

Fig. 2. Population density of people (P), rats (R), and trees (T) as a function of position around the ring at a fixed time.

Figure 3

Fig. 3. Population density of people as a function of position around the ring (s) and time (t). Time is in units of years, and the lighter regions correspond to greater population.
Figure 4

Fig. 4. A projection of the strange attractor at a typical place around the ring, showing the population density of rats (R) versus the population density of people (P) with the population density of trees indicated by a shadow.
Figure 5

Fig. 5. Attractors showing a progression from a simple limit cycle at D = 0 to a period-2 limit cycle at D = 0.008 to a period-4 limit cycle at D = 0.0083 to chaos at D = 0.009.