The possible states of a population of eusocial insects

Abstract

A controlled dynamical system describing the growth of a population of eusocial insects is discussed. The approach differs in two ways from previous work. First, the full reachable set is determined (rather than just the optimal control maximizing the number of reproducibles). Second, a time-dependent coordinate transformation is used which renders the system non-autonomous, but eases the analytical derivation of the result. Finally, we comment on educational aspects which arose from the classroom use of the example discussed and report on the positive experiences made.