Two simple models of constrained growth, showing how stable structure arises through coupling positive feedback of one order with negative feedback of a higher order. This mechanism forms the basis of all stable states (and therefore of all memory) in nature.
In the first model a Protein is expressed at a constant growth rate betaP, and is degraded exponentially - that is, at a rate alphaP * Protein which is directly proportional to its current concentration. The result is the so-called 'leaky barrel' model, which grows to a stable value of betaP/alphaP.
In the second model Rabbits are born at a rate betaR * Rabbits which is proportional to the current number of Rabbits, but due to competition they die hyperexponentially (i.e. proportional to the square of the number of Rabbits). The result is the logistic model, which grows to a stable value of betaR/alphaR.