Dynamics of the Consensus Model of Rotifer Populations: Bifurcation Portrait
by
F. Berezovsky
Department of Mathematics, Howard University Washington D.C. 20059, USA
Coauthors: G. Karev (National Institute of Health, Bethesda MD 20894), M.Borodovsky, T.Snell (School of Biology Georgia Institute of Technology, Atlanta GA 30332-0145)

Model based on the real data from natural populations of nine zooplankton species [1] was derived by computer system RAMAS and presented as a discrete nonlinear map:

N(t+1) = exp(r(N(t))N(t), with r(N)=-a + 1/N – g/N2

where parameters g is species-specific and a characterizes environmental conditions. Model dynamics and their change with variations of parameters were investigated with analytical [2] and computer approaches [3]. A bifurcation portrait of the model was constructed, eight parameter domains of qualitavely different behaviors were found from which domains of population persistence (stable equilibrium, periodic and a- periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to the critical parameter values were given and discussed.

1.Snell T.W., M. Serra (1998). Dynamics of natural rotifer populations. Hydrobiologia. 368: 29-35.

2.Devaney R.L. (1989). An Introduction to Chaotic Dynamical Systems. Addison-Wesley Publishing Company.

3.Levitin V. (1987). TRAX: Simulation and Analysis of Dynamical systems. NY.: Exeter Publishing.

Date received: February 23, 2003