The first part of this paper is devoted to a complete description of the dynamics of a continuously structured population model coupled with a dynamical resource. In the model, it is assumed that the energy each individual obtains from the resource is channeled between growth and reproduction in a proportion that depends on the individual's size. In the second part, an optimal allocation of this energy is obtained that turns out to be a convergence-stable ESS and is described by what is called a `bang-bang' strategy.
Calsina, À., & Saldaña, J. (1999). Global dynamics and optimal life history of a structured population model. SIAM Journal on Applied Mathematics, 59, 1667-1685. https://doi.org/10.1137/S0036139997331239