While on Route to Bermuda

日期:2014/03/18

While on route to Bermuda, I whiled away the time by studying the logistic equation which models the growth of a population when constrained by space, resources, and competition. I read section 1-5 of Braun's excellent book Differential Equations. The formulation that Braun uses which is general is dp/dt = ap - b ( p) x (p). The curve grows to a limiting value of a/b. It grows at an increasing rate to 1/2 x ( a/b) and then starts decreasing. Its graph is called a logistic or an s shaped curve. It models very well the growth of innovation, the growth of salmon when confronted by sharks, and the start of epidemics, when p ? A/b. This is relatively elementary to those who study population models, but I found that many companies with innovative products seem to follow the logistic curve, and many markets seem to follow the curve with a lag when confronted by startling movements in other markets. I wonder if fitting logistic curves to markets and companies under appropriate conditions would be of use for prediction? As for Bermuda, a country with no income service rate, no unemployment, and no welfare, and great prosperity and civility, conformity is the norm. One was fortunate not to be expelled, one believes.