A stage structure model for the growth of a population involving switching and cooperation

We propose a theoretical model for a predator-prey interaction where the prey is a stage-structured population with varying maturity times for the immature stage. The interaction terms between immatures and adults are interpreted as cooperation. The predator consumes both the young and the adult of the prey and this prey population is more prone to predation at higher densities. The existence and stability of the equilibrium set are discussed. Using maturity time as a bifurcation parameter it is shown that Hopf bifurcation could occur.