The interdisciplinary
and emerging field of nonlinear dynamics offers new strategies and paradigms
for understanding complex systems like the human brain and its relation to mind
and behavior. For example, it now appears that pattern formation and self-organization
in nonequilibrium physical, chemical and biological systems may be governed
by a number of general principles. This emphasis in the natural sciences on
structure formation in complex systems is bridging the gap between what one
element does and what many of them do when they function cooperatively.The goal
of neuroscience, since its early beginnings, has been to do the same for neurons
and neuronal groups. Neuroscience must now be supplemented with new mathematical
ideas, research strategies and computational tools, if the inherent complexity
of the most complex system of all - the human brain and its relation to cognition
and behavior - are to be understood.
Observations
of phenomena in neuroscience range from fractions of milliseconds of ion channel
dynamics to days and months of memory formation in the temporal domain. In physical
space, observations range from the molecular level to brain patterns of several
centimeters size observed in EEG and MEG. This vast complexity in space and
in time can only be studied and understood under the guidance of theoretical
models which allow the identification of the underlying mechanism of the experimentally
observed phenomena. Such models may be developed for the same phenomena on different
levels of description. For example, in the mid 1980s bimanual coordination dynamics
has been understood in terms of nonlinearly coupled oscillators describing the
periodic motion of limbs phenomenologically. In the late 1990s it became possible
to derive this behavioral model from models which describe the processes in
the brain during bimanual coordination, i.e. its neural correlates. Such
a connection among scales of organization proves to be powerful, since individual
descriptions of brain and behavioral dynamics do not have to stand on their
own, but together tell a whole story on how brain and behavior determine each
other.
