Cobweb diagram for the Logistic Equation
This is a difference equation or recurrence equation, it relates “one value to the previous value(s)”1. It looks deceptively simple, but because it’s non-linear (product of two linear functions), we need to be a little careful with it. We will soon find out how nasty it can become. But before that why is it important? This equation is a population model; xn is the ratio between the actual population and the maximum population, so 0 ≤ xn ≤ 1. λ is a positive factor which combines both ‘birth rate’ and ‘death rate’. For xn to satisfy its restrictions, we need to restrict λ to 0 ≤ λ ≤ 4. So for example if we found λ of a population, then we could use this model to find out if the population will extinct, settle to fixed number or overpopulate.