7 Positive feedback

Example 1. (Bird populations) Let $x$ be the number of birds on an isolated island, say puffins on Ailsa Craig. The birth rate of birds is proportional to the number of birds, and birds can come and go by flying to other nesting sites at rate $u$, so, for some $k>0$,

Example 2. (Turbocharger) A car engine has a turbocharger. The faster the engine revolves, the more exhaust it produces, so the turbo forces more air into the engine, so the engine goes faster and so on.

Most practical devices incorporate some negative feedback so that they do not damage themselves or their users.

Example 3. (Black’s amplifier) Let . The output $y$ is fed back into the input $u$, after multiplication by $\theta$, so $y=\theta y+u$, hence $y=u/(1-\theta )$ is an amplified version of the input.