The central aim of this thesis is to better understand the dynamics of a set of dynamically
coupled map systems previously introduced by Ito & Kaneko in a series of papers (Phys.
Rev. Lett. 88 (2002), no. 2, 028701 and Phys. Rev. E 67 (2003), no. 4, 046226). The current
work extends Ito & Kaneko’s studies to clarify the changes in macrodynamics induced
by the differences in microdynamics between the two systems. A third system is also
introduced that has a minor change to the microdynamics from nonlinear to linear output
function in the externally coupled system.
The dynamics of these three dynamically-coupled maps is also compared with their
simplified systems with static coupling. The previous studies of these dynamically-coupled
maps showed a partitioning of the parameter space into regions of different macrodynamics.
Here, an in-depth study is presented of the behaviour of the systems as they cross the
boundary between one region and another. The behaviour across this boundary is shown to
be much more complicated than suggested in the previous studies.
These three systems of dynamically-coupled maps all differ in the form of their microscopic
couplings, yet two of the systems are shown to produce similar macrodynamics,
whereas the third differs dramatically by almost any measure of the macrodynamics.
The time it takes for the systems to synchronise, both the dynamically-coupled and
static-coupled systems, is investigated. It is shown that the introduction of dynamicalcouplings
stops the systems from synchronising quasi-instantaneously. Details of potential
consequences of this in the field of neuroscience are discussed.
A brief study of the effect of driving the systems with external stimuli is presented.
The different microscopic coupling forms cause different responses to the external stimuli.
Some of the responses are similar to that observed by the visual cortex area of the brain
