encouragement: the more Romeo seems to like her, the more she likes him. It’s easy to see that the story’s outcome given this behavior will be far different than the outcome in which their affections are purely driven by mutually reinforcing positive feedback loops. Rather than growing without bound, their affections will tend to stabilize at a particular level, the precise nature of which is determined by two factors: the initial conditions (how much they like each other to begin with), and the level of responsiveness by each teen (how much Juliet’s affection responds to Romeo’s reciprocity, and how much Romeo’s affection responds to Juliet’s enthusiasm). Depending on the precise tuning of these values, the relationship may either stabilize in a mutually congenial way (as both lovers are drawn toward a middle ground of passion), or it may stabilize in a way that results in the relationship ending (as Romeo’s lack of interest frustrates Juliet and she gives up). In either case, the important feature of the example is its eventual movement toward a stable attractor.
5.2.2 The Role of Feedback Loops in Driving Climate Dynamics
Similar feedback mechanics play central roles in the regulation and evolution of the global climate system. Understanding the dynamics and influence of these feedback mechanics is essential to understanding the limitations of basic models of the sort considered in Chapter Four. Some of the most important positive feedback mechanics are both obvious and troubling
- Under some conditions, the situation described here might fall into another class of attractors: the limit cycle. It is possible for some combinations of Romeo and Juliet’s initial interest in each other to combine with features of how they respond to one another to produce a situation where the two constantly oscillate back and forth, with Romeo’s interest in Juliet growing at precisely the right rate to put Juliet off, cooling his affections to the point where she once again finds him attractive, beginning the cycle all over again. In either case, however, the stability of the attractor is the important feature is the attractor’s stability. Both the two fixed-point attractors described in the text (the termination of the courtship and the stabilization of mutual ) result in the values of the relevant differential equations “settling down” to predictable behavior. Similarly, the duo’s entrance into the less fortunate (but just as stable) limit cycle represents predictable long-term behavior.