I propose a new theory of leadership in complex systems based upon computational modeling approaches that have appeared to date. It is new in that it promises an approach that is well specified, coherent across levels of analysis, is transparent to the outside observer and can be modeled computationally. Although many of its independent components have been modeled, the underlying theory connecting these models is articulated here for the first time. Leadership is defined as those aspects of agent interactions which catalyze changes to the local rules defining other agents' interactions. There are five distinct aspects of leadership to be observed. Leadership involves actions among agents that: (a) identify or espouse a cooperation strategy or program, (b) catalyze conditions where other agents choose to participate in the program, (c) organize choices and actions in other agents to navigate complexity and avoid interaction catastrophe (sometimes called "complexity catastrophe"), (d) form a distinct output layer that expresses the system as a unity in its environment, and (e) translate feedback into structural changes in the influence network among agents. The contribution of this approach is discussed.