Amplitude death in complex networks induced by environment

We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment-like external system. We develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death. An important outcome of our study is a universal relation between the critical coupling strength and the largest non-zero eigenvalue of the coupling matrix. Our results are fully supported by the detailed numerical analysis for different network topologies.