Spatiotemporal Chaos in Easter Island Ecology
J. C. Sprott
Department of Physics
University of Wisconsin, Madison
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
The complete paper is available in
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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.
Fig. 2. Population density of people (P
), rats (R
and trees (T
) as a function of position around the ring at
a fixed time.
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
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.
Fig. 5. Attractors showing a progression from a simple limit cycle
= 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