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We present a mechanism for amplitude death in coupled nonlinear dynamicalsystems on a complex network having interactions with a common environment-likeexternal system. We develop a general stability analysis that is valid for anynetwork topology and obtain the threshold values of coupling constants for theonset of amplitude death. An important outcome of our study is a universalrelation between the critical coupling strength and the largest non-zeroeigenvalue of the coupling matrix. Our results are fully supported by thedetailed numerical analysis for different network topologies.

Amplitude death in complex networks induced by environment