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CAM colloquium - Friday, October 14 --NOTE
TIME AND ROOM
12:00 p.m.
253 Rhodes Hall
Speaker: Gabor Domokos
Budapest Univ. of Technology and Economics
Title: Discrete state models in chaotic population dynamics
Abstract:
G. Domokos (Budapest Univ. of Technology and Economics)
I. Scheuring (Eotvos University, Budapest)
Both time and population size can be treated either as discrete
or continuous in population dynamics. Traditionally, time was chosed
according to the character of the population, however, the size was
always considered as a real number. Recently, it became obvious that
if the dynamics is chaotic, integer-based discrete models give radically
different predictions. Real populations obviously consist of integer
numbers of individuals, however, it is equally obvious that random
noise has to be added to the deterministic model. Such noisy, discrete
models display ambivalent behaviour. In case of low noise they resemble
the discrete deterministic models, in case of high noise they predict
statistics similar to the continuous model. In real populations the
noise is intermediate, and models in this intermediate zone show complex
behaviour. Using recent results from the theory dynamicals systems
as well as experimental data from the Beetle Team we propose some
qualitative explanations and guidelines for numerical simulations.
References:
Henson, S. H., Costantino, R. F.,Cushing, J. M., Deshernais R. A.,Dennis,
B. \& King, A. A: Lattice effect observed in chaotic dynamics
of experimental populations. Science Vol. 294, 602--605. (2001)
G. Domokos, I. Scheuring: Random Perturbations and Lattice Effects
in Chaotic Population Dyamics. Science Vol 297,
No.5590,p2163 (Sept 27 2002)
G. Domokos, D. Szasz: Ulam's scheme revisited: digital modeling of
chaotic attractors via micro-perturbations. Discrete and Continuous
Dynamical Systems, Ser. A. Vol 9. No.4. Pp 859-876 (2003).
Henson, S. H., King, A. A., Costantino, R. F., Cushing, J. M., Dennis,
B. & Deshernais R. A.: 2003. Explaining and predicting patterns
in stochastic population systems. Proc. Roy. Soc. Ser. B. {270}, 1549--1553
(2003)
G. Domokos, I. Scheuring: Discrete and continuous state population
models in a noisy world. J. Theoretical Biology,
Vol 227, pp 535-545. (2004)
I. Scheuring, G. Domokos: Sturdy cycles in the chaotic Tribolium castaneum
data series.Theor. Pop. Dyn. 67 (2005) pp 127-139.
Refreshments at 1:00 p.m. in 657 Rhodes Hall.
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