On the stability of adjustment processes with persistent randomness

Most distributed systems and systems depending on their sensing of their surroundings operate under a great deal of uncertainty from many sources. The dynamic behavior of such systems can assume very complex forms inducing complex dynamics that are challenging to observe and control. This is mainly due to noisy data received from the environment in which they evolve, data that has to be fed back to their decision support. These closed and endless feedback loops are prone to error if not dealt with in an appropriate manner. The nonlinearity of circular causation and feedback effects of such phenomenon creates an environment where some models, driven by practicality concerns, resort to simplification strategies that ignore important feedback relationships, but make the decision problem more tractable. Even so, the non-smooth dynamics of such systems makes stability analysis difficult. The consequence hereof is the existence of models that are constrained to the brink of loosing their true purpose. In this paper, we present a cross-fertilization approach using tools from physics and biology to show how one can practically approach the stability analysis of such systems.