Chaos in Easter Island Ecology
J. C. Sprott
Department of Physics
University of Wisconsin, Madison
This paper demonstrates that a recently proposed dynamical 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 15, 445-454
The complete paper is available in
Return to Sprott's Books and Publications.
Fig. 1. History of the people (P) and trees (T) predicted by the
Brander-Taylor Model. Time is in units of 250 years, and the human
population peaks at a value of about 10,000 people.
Fig. 2. History of the people (P) and trees (T) predicted by the
Basener-Ross Model. Time is in units of millennia, and the
population peaks at a value of about 9400 people.
Fig. 3. A periodic solution predicted by the Basener-Ross Model.
The unit of time is about 7 years, and the human population
oscillates between about 1300 and 30,000 people.
Fig. 4. A chaotic solution predicted by the Invasive Species
Model. The unit of time is years, and the human population
averages about 7200 people.
Fig. 5. A return map showing the minimum human population versus
the previous minimum for the chaotic Invasive Species Model.
Fig. 6. Largest Lyapunov exponent and minimum value of the human
population as a function of the tree-harvest rate for the Invasive
Species Model shows a period-doubling route to chaos followed by
Fig. 7. State space plots for the Invasive Species Model at
increasing values of the harvesting rate showing successively
attraction to the coexisting equilibrium, a simple limit cycle, a
period-doubled limit cycle, a chaotic attractor, transient chaos,
and rapid extinction.
Fig. 8. Population of people (P), rats (R), and trees (T)
permitted by the Invasive Species Model as a function of tree
harvesting rate, showing the narrow region of periodic and chaotic
oscillations preceding the crash.