Competition with Evolution in Ecology and Finance
J. C. Sprott
Department of Physics, University
of Wisconsin- Madison, Madison, WI 53706, USA
(Received 9 December 2003; received in revised form 11 March 2004;
accepted
12 March 2004)
ABSTRACT
A variant of the multi-species Lotka–Volterra model is studied in which
species competing for fixed finite resources are replaced by new
randomly
chosen species whenever they become extinct. The model exhibits chaos,
punctuated equilibria, leptokurtosis, and self-organized criticality.
It
has application to ecology, finance, and possibly other diverse
systems.
Ref: J. C. Sprott, Phys. Lett. A 325,
329-333 (2004)
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Fig. 1. Typical temporal variation of 48 species without evolution.
Fig. 2. Fluctuations in average biomass and biodiversity for 48
species
with evolution.
Fig. 3. Fluctuations in biomass for two initial conditions that
differ
by 10-9.
Fig. 4. Fluctuation of the stock market (1930-2002), a Gaussian
distribution,
and the model, all normalized to the same standard deviation.
Fig. 5. Probability distribution function of volatility showing a
power-law
scaling.
