Age-structured predator-prey model with habitat complexity: oscillations and control

In this article, we study a predator-prey interaction in a homogeneously complex habitat where predator takes a fixed time to develop from immature to its mature stage. The age-structure of the predator and its interaction with the prey is framed in a system of delay differential equations. The objective is to study the role of habitat complexity and the maturation delay of the predator on the overall dynamics of the model system. Different interesting dynamical behaviours can be obtained by regulating two key parameters, namely the degree of habitat complexity and the maturation delay. It is observed that the system becomes unstable from its stable condition when the maturation delay crosses some critical value. The periodic solutions bifurcated from the interior equilibrium is found to be supercritical and stable. Synchronization of population fluctuations is, however, possible by increasing the strength of habitat complexity. The predator population goes to extinction and the prey population reaches to its maximum, irrespective of the length of maturation delay, when the habitat complexity crosses some upper critical value. The qualitative dynamical behaviours of the model system are verified with the data of Paramecium aurelia (prey) and Didinium nasutum (predator) interaction.