Zahra Aminzare, University of Iowa
Abstract: Synchronization refers broadly to patterns of coordinated behaviors that emerge spontaneously or by design in natural and artificial complex network systems. Network synchronization can arise from the dynamics of the isolated individuals, exogenous control inputs, the properties of the interconnection among the individuals, and the topological structure of the network. Contraction Theory is a powerful tool to characterize and analyze the stability properties of synchronization patterns in networks of nonlinear systems. First, I will review contraction theory for deterministic systems, generalize it to Itô stochastic differential equations, and show how noise can induce contractivity in a system. Then, using contraction theory, I discuss the emergence of synchronization patterns in networks of deterministic and stochastic nonlinear systems.