Feedback intensity and leader-follower behavior: A mathematical description

Abstract

A mathematical model of feedback-controlled behavior is developed using minimal assumptions about the nature of the leader-follower system. The essential element is that the system is linked through consistent feedback based on the follower's behavior. The model shows that the follower can exhibit convergent, periodic or chaotic patterns of behavior. If the leader's feedback is based on an incentive function that varies strongly with output, or if the follower strongly discounts the leader's feedback, then the follower's behavior may not be predictable. Thus, seemingly random behavior can result from entirely consistent, deterministic conditions. This conclusion applies equally well to cases where the leader and the follower are singular or aggregate entities such as biological or social systems. The behavioral pattern that is exhibited depends on the value of a single constant, which is the product of the follower's reactivity to incentives and the leader's incentive change rate. The fact that a single constant can be used to differentiate between fundamentally different forms of behavior is important to the study of leadership.