A theoretical study of different leader roles in networks

We study synchronization conditions for distributed dynamic networks with different types of leaders. The role of a "power" leader specifying a desired global state trajectory through local interactions has long been recognized and modeled. This note introduces the complementary notion of a "knowledge" leader holding information on the target dynamics, which is propagated to the entire network through local adaptation mechanisms. Different types of leaders can coexist in the same network. For instance, in a network of locally connected oscillators, the power leader may set the global phase while the knowledge leader may set the global frequency and the global amplitude. Knowledge-based leader-followers networks have many analogs in biology, e.g., in evolutionary processes and disease propagation.