Much mathematical modelling has involved the assumption that physical systems are
approximately linear, leading to the construction of equations which, although relatively easy
to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear
systems, however, lead to the emergence of new structures that reflect reality much more
closely. This second edition of Nonlinear Science, covers several important areas of
nonlinear science, and places a strong emphasis on applications to realistic problems. It …

The activity of a human brain is organized into many levels, from the dynamics of individual
membrane proteins, through the switching of isolated patches of membrane and collisions
among propagating nerve impulses, to the complex interactions of the neocortex with human
culture. 1 A key concept in understanding these dynamics is that of a cell assembly of
neurons, which was defined by Donald Hebb as follows: 2 Any frequently repeated,
particular stimulation will lead to the slow development of a 'cell-assembly,'a diffuse structure …