  Dynamics with a threshold input--output relation commonly exist in gene,
signal-transduction, and neural networks. Coupled dynamical systems of such
threshold elements are investigated, in an effort to find differentiation of
elements induced by the interaction. Through global diffusive coupling, novel
states are found to be generated that are not the original attractor of
single-element threshold dynamics, but are sustained through the interaction
with the elements located at the original attractor. This stabilization of the
novel state(s) is not related to symmetry breaking, but is explained as the
truncation of transient trajectories to the original attractor due to the
coupling. Single-element dynamics with winding transient trajectories located
at a low-dimensional manifold and having turning points are shown to be
essential to the generation of such novel state(s) in a coupled system.
Universality of this mechanism for the novel state generation and its relevance
to biological cell differentiation are briefly discussed.
