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In this paper, we discuss distributed adaptive algorithms for synchronizationof complex networks, consensus of multi-agents with or without pinningcontroller. The dynamics of individual node is governed by generalized QUADcondition. We design new algorithms, which can keep the left eigenvector of theadaptive coupling matrix corresponding to the zero eigenvalue invariant. Basedon this invariance, various distributive adaptive synchronization, consensus,anti-synchronization models are given.

Adaptive algorithms for synchronization, consensus of multi-agents and anti-synchronization of direct complex networks