  Characterizing the emergence of chaotic dynamics of complex networks is an
essential task in nonlinear science with potential important applications in
many fields such as neural control engineering, microgrid technologies, and
ecological networks. Here, we solve a critical outstanding problem in this
multidisciplinary research field: The emergence and persistence of
spatio-temporal chaos in complex networks of damped-driven nonlinear
oscillators in the significant weak-coupling regime, while they exhibit regular
behavior when uncoupled. By developing a comprehensive theory with the aid of
standard analytical methods, a hierarchy of lower-dimensional effective models,
and extensive numerical simulations, we uncover and characterize the basic
physical mechanisms concerning both heterogeneity-induced and impulse-induced
emergence, enhancement, and suppression of chaos in starlike and scale-free
networks of periodically driven, dissipative nonlinear oscillators.
