Network Synchronization with Convexity
Provides theoretical synchronization conditions for complex networks with nonlinear dynamics and switching directed graphs, relevant to control and network science communities.
This paper establishes new synchronization conditions for complex networks with nonlinear, nonidentical node dynamics and switching directed communication graphs, showing that when node self-dynamics are gradients of concave functions, exact or approximate synchronization can be achieved under relaxed connectivity requirements.
In this paper, we establish a few new synchronization conditions for complex networks with nonlinear and nonidentical self-dynamics with switching directed communication graphs. In light of the recent works on distributed sub-gradient methods, we impose integral convexity for the nonlinear node self-dynamics in the sense that the self-dynamics of a given node is the gradient of some concave function corresponding to that node. The node couplings are assumed to be linear but with switching directed communication graphs. Several sufficient and/or necessary conditions are established for exact or approximate synchronization over the considered complex networks. These results show when and how nonlinear node self-dynamics may cooperate with the linear diffusive coupling, which eventually leads to network synchronization conditions under relaxed connectivity requirements.