Stability Analysis
When you put a cold drink on the kitchen counter the counter surface temperature will decrease. But, if the cold drink is removed, the counter will eventually return to room temperature. If instead we place a cup of tea on the counter, the counter temperature rises; but if we remove the cup of tea, the counter top eventually returns to room temperature. We say that the counter at room temperature is a stable equilibrium. In this video, we discuss the world from the perspective of equilibrium and stability, and in particular linear stability. This video is part of the Linearity video series. Many complex systems are modeled or approximated as linear because of the mathematical advantages. All the world is an initial value problem, and the matter merely state variables. However, and less poetically, there are alternative interpretations of physical, and indeed social, systems that can prove very enlightening. The purpose of this video is to introduce you to the framework of...