Niels Bohr Institutet > Kalender - det sker på NBI > 2010 > Master´s thesis defenc...

Master´s thesis defence by Pia Cordsen

Small networks or “motives” are the building blocks of large networks
such as genetic signalling proteins, ecological and economic systems. Understanding
simple motif dynamics can be a first step to understand large
networks. Here an investigation of the symbolic dynamics of ecologically
inspired motives consisting of only 3 interacting species is presented. In
this context ’symbolic dynamics’ means a characterization of the system
dynamics in terms of maxima and minima of the species densities. Examples
of the symbolic dynamics found when exploring the parameter space
of the Hastings-Powell model are presented along with a set of rules for
allowed symbolic dynamics transitions.

Two other 3-species motives are presented, one motif with 2 predators
and 1 prey, the other with 2 preys and 1 predator. The competitors are
assigned identical governing equations, so that when the parameters are
equal, the system is symmetrical. From here, 1 parameter at a time is
tuned to observe the effect on the dynamics of this introduced asymmetry.
The main result presented is that for parameter values allowing for longterm
coexistence, the better competitor peaks first. The results presented
here show that the coarse graining method of symbolic dynamics provides
systematic insight into the dynamics of small systems that are otherwise
beyond systematic mathematical treatment because analytical solutions
cannot be found.