# Numberphile: Feigenbaum constant

Last time when we wrote about Lotka-Volterra equations, we have mentioned Verhulst's model of population dynamics, given by

\begin{equation} \mathrm{d} x = r x ( 1 – x ) \mathrm{d} t, \end{equation}

which describes temporal evolution of ecological systems with limited supply of food. The model has parameter \( r \) which controls the availability of food to the population. It would be natural to ask how the availability of food impacts the dynamics of model? Does the population converge? If so, then to which state? May be the population does not converge? How do the answers to these questions change based on model parameter? More on this and the interesting mathematics in this Numberphile video.