Fred J Molz
Clemson University, USA
Title: An exploratory mathematical analysis of deterministic chaotic dynamics in a four-component microbial system
Biography
Biography: Fred J Molz
Abstract
We apply an exploratory mathematical analysis to study the observed presence of chaotic dynamics involving a nutrient, two competing prey microbes (rods and cocci) and a ciliate predator in a chemostat. To begin, we generalized the Kot et al. (1992) fully mixed, differential equation system (nutrient plus 2 microbes) to a nutrient plus three microbes system. This first generalization tended to produce solutions wherein only two microbes survived, so the Monod functions representing growth kinetics (specific growth and consumption rates) were modified to have the maximum specific growth rates decrease slightly with growth. This allowed all 3 microbes to survive, but did not produce chaotic dynamics unless, following Kot et al. (1992), the feeding rate was made sinusoidal in time. Internally-generated deterministic chaos, as occurred in the Becks et al. experiments, was finally obtained by (a) causing the predator’s preference for rods to increase by a factor of 4 with increasing prey species populations, and (b) allowing the rods to outcompete the cocci for nutrient by a factor of 1.5 in maximum specific growth rates. The presence of low-dimensional deterministic chaos in time series data was verified by calculating the correlation dimension, embedding dimension and a spectrum of Lyapunov exponents. We also discuss how the formation of a strange attractor within a biological context may be interpreted as a type of emergence, and that modern information theory may imply that deterministic chaotic dynamics is the underlying basis for healthy (sustainable?) biological systems.