  This article outlines sufficient conditions under which a one-dimensional
chain of identical nonlinear oscillators can display complex spatio-temporal
behavior. The units are described by phase equations and consist of excitable
oscillators. The interactions are local and the network is poised to a critical
state by balancing excitation and inhibition locally. The results presented
here suggest that in networks composed of many oscillatory units with local
interactions, excitability together with balanced interactions are sufficient
to give rise to complex emergent features. For values of the parameters where
complex behavior occurs, the system also displays a high-dimensional
bifurcation where an exponentially large number of equilibria are borne in
pairs out of multiple saddle-node bifurcations.
