Distributed coordination and partial synchronization in complex networks

Motivated by coordinating behavior widely observed in nature, this thesis studies stochastic distributed coordination algorithms and partial synchronization in complex networks. Distributed coordination algorithms are usually under inevitable random influences or deliberately randomized to improve performance. Such dynamical processes are usually modeled by stochastic discrete-time dynamical systems. In the first part of this thesis, we propose some new criteria, termed finite-step Lyapunov criteria, for the stability and convergence analysis of stochastic discrete-time systems, and then use them to study the convergence of several distributed coordination algorithms. As a special type of coordinating behavior, partial synchronization is believed to occur in the human brain more commonly than global synchronization. With the help of the Kuramoto model and its variations, we analytically study partial synchronization in the second part. Two cases, i.e., partial synchronization among directly connected regions and among regions that has no direct links, are both considered. To analyze the latter one, some new criteria for partial stability of slow-fast nonlinear systems are also developed